How do you differentiate #g(x) = (2sinx e^x) ( 2xx^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:
 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:
 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:
 Identify the functions (To 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:
 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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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:

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 ).

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

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

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:

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 ).

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

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

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:

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 ).

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

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

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:

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 ).

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

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

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:

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 ).

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

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

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:

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 ).

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

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

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:

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 ).

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

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

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:

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 ).

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

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

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:

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 ).

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

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

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:

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 ).

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

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

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:

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 ).

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

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

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:

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 ).

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

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

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:

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 ).

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

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

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:

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 ).

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

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

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) ).

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 ).

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) ).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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