How do you differentiate #g(x) = (2sinx -e^x) ( 2x-x^2)# using the product rule?

The product rule tells us:

We have the two products and there derivatives:

and

So on substitution into the chain rule formula we get:

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To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(gTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1.To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify theTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)hTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functionsTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(xTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions (To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

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1. Identify the functions ( uTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))'To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(xTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' =To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x)To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = gTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) \To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) )To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(xTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) andTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and (To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)hTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( vTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(xTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(xTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x)To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x)To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) +To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let (To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + gTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( uTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(xTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(xTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x)To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)hTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) =To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(xTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

FirstTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sinTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First,To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin xTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identifyTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x -To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify gTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - eTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(xTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x)To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^xTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) =To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x \To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x )To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) andTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and (To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinxTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( vTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx -To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(xTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) =To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x)To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - xTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) =To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

NextTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 \To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next,To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, findTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find theTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2.To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivativesTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. ComputeTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives ofTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute theTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of gTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivativesTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(xTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives ofTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x)To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of (To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) andTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( uTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and hTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(xTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(xTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x)To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) \To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

gTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) )To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) andTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(xTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and (To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x)To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( vTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) =To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(xTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x)To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) \To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosxTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx -To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). (To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - eTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( uTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^xTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(xTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x)To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x)To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) andTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) =To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and hTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(xTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x)To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cosTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) =To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos xTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x -To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - eTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 -To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^xTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x)To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2xTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) \To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) )To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

FinallyTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) andTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally,To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and (To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substituteTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( vTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute theseTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these valuesTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(xTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values intoTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x)To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into theTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) =To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the productTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product ruleTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formulaTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 -To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

gTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2xTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(xTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x \To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)hTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(xTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3.To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x)To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. ApplyTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) +To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply theTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + gTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the productTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(xTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product ruleTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formulaTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)hTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(xTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: (To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x)To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( gTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) =To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(xTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x)To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) =To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosxTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = uTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx -To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(xTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - eTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)vTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^xTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(xTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x)To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) +To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2xTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + vTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x -To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(xTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - xTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - x^To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)uTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - x^2To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)u'(To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - x^2)To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)u'(xTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - x^2) +To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)u'(x)To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - x^2) + (To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)u'(x) \To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - x^2) + (2To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)u'(x) ).

To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - x^2) + (2sinTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)u'(x) ).

4To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - x^2) + (2sinxTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)u'(x) ).

4.To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - x^2) + (2sinx -To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)u'(x) ).

4. SubstituteTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - x^2) + (2sinx - eTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)u'(x) ).

4. Substitute theTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - x^2) + (2sinx - e^To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)u'(x) ).

4. Substitute the derivativesTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - x^2) + (2sinx - e^xTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)u'(x) ).

4. Substitute the derivatives andTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - x^2) + (2sinx - e^x)(To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)u'(x) ).

4. Substitute the derivatives and theTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - x^2) + (2sinx - e^x)(2To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)u'(x) ).

4. Substitute the derivatives and the originalTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - x^2) + (2sinx - e^x)(2 -To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)u'(x) ).

4. Substitute the derivatives and the original functionsTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - x^2) + (2sinx - e^x)(2 - To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)u'(x) ).

4. Substitute the derivatives and the original functions intoTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - x^2) + (2sinx - e^x)(2 - 2To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)u'(x) ).

4. Substitute the derivatives and the original functions into theTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - x^2) + (2sinx - e^x)(2 - 2xTo differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)u'(x) ).

4. Substitute the derivatives and the original functions into the formulaTo differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - x^2) + (2sinx - e^x)(2 - 2x).To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)u'(x) ).

4. Substitute the derivatives and the original functions into the formula: To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - x^2) + (2sinx - e^x)(2 - 2x).To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)u'(x) ).

4. Substitute the derivatives and the original functions into the formula: To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - x^2) + (2sinx - e^x)(2 - 2x).To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)u'(x) ).

4. Substitute the derivatives and the original functions into the formula: (To differentiate the function g(x) = (2sinx - e^x)(2x - x^2) using the product rule, you apply the formula:

(g(x)h(x))' = g'(x)h(x) + g(x)h'(x).

First, identify g(x) = (2sinx - e^x) and h(x) = (2x - x^2).

Next, find the derivatives of g(x) and h(x):

g'(x) = (2cosx - e^x) and h'(x) = (2 - 2x).

Finally, substitute these values into the product rule formula:

g'(x)h(x) + g(x)h'(x) = (2cosx - e^x)(2x - x^2) + (2sinx - e^x)(2 - 2x).To differentiate ( g(x) = (2\sin x - e^x)(2x - x^2) ) using the product rule, follow these steps:

1. Identify the functions ( u(x) ) and ( v(x) ) within the expression. Let ( u(x) = 2\sin x - e^x ) and ( v(x) = 2x - x^2 ).

2. Compute the derivatives of ( u(x) ) and ( v(x) ). ( u'(x) = (2\cos x - e^x) ) and ( v'(x) = 2 - 2x ).

3. Apply the product rule formula: ( g'(x) = u(x)v'(x) + v(x)u'(x) ).

4. Substitute the derivatives and the original functions into the formula: ( g'(x) = (2\sin x - e^x)(2 - 2x) + (2x - x^2)(2\cos x - e^x) ).

5. Expand and simplify the expression: ( g'(x) = 4\sin x - 4x\sin x - 2e^x + 2xe^x + 4x\cos x - 2x^2\cos x - 2x\sin x + x^2\sin x ).

6. Combine like terms to get the final result: ( g'(x) = (4\sin x + 4x\cos x - 2e^x + 2xe^x) - (2x^2\cos x + 2x\sin x - x^2\sin x) ).