# How do you use the product Rule to find the derivative of #(2x)(-sinx) + (cosx)(2) - 2(cosx)#?

First of all, notice how this cancels to give:

Much easier now. Using the product rule, you have:

So, you get:

By signing up, you agree to our Terms of Service and Privacy Policy

To find the derivative using the product rule, apply the formula:

[ \frac{d}{dx} [f(x)g(x)] = f'(x)g(x) + f(x)g'(x) ]

Given ( f(x) = 2x ) and ( g(x) = -\sin(x) ), the derivatives are ( f'(x) = 2 ) and ( g'(x) = -\cos(x) ).

[ \frac{d}{dx} [2x(-\sin(x))] = (2)(-\sin(x)) + (2x)(-\cos(x)) ]

Given ( f(x) = \cos(x) ) and ( g(x) = 2 ), the derivatives are ( f'(x) = -\sin(x) ) and ( g'(x) = 0 ).

[ \frac{d}{dx} [\cos(x)(2)] = (-\sin(x))(2) + (\cos(x))(0) ]

Finally, given ( f(x) = -2 ) and ( g(x) = \cos(x) ), the derivatives are ( f'(x) = 0 ) and ( g'(x) = -\sin(x) ).

[ \frac{d}{dx} [-2\cos(x)] = (0)(\cos(x)) + (-2)(-\sin(x)) ]

Summing up these results, we get the derivative:

[ \frac{d}{dx} [2x(-\sin(x)) + \cos(x)(2) - 2\cos(x)] = -2\sin(x) + 2x(-\cos(x)) - 2\sin(x) ]

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided 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 one-sided 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 one-sided 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.

- How do you find the derivative of the function #y=sin(tan(4x))#?
- How do you find #(dy)/(dx)# given #x^3+y^3=3xy^2#?
- How do you differentiate #(z) = (sqrt16z) / ((17z - 5) ^(3/2))#?
- What is the derivative of #sqrt(t^5) + root(4)(t^9)#?
- If #f(x) =sec^2(x/2) # and #g(x) = sqrt(5x-1 #, what is #f'(g(x)) #?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7