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

For two functions, the product rule is

Now divide and make things easier.

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

To differentiate ( f(x) = (e^x + x)(x^2 - x) ) using the product rule, apply the formula ( (uv)' = u'v + uv' ). Let ( u = e^x + x ) and ( v = x^2 - x ). Then, differentiate ( u ) with respect to ( x ) to get ( u' ), and differentiate ( v ) with respect to ( x ) to get ( v' ). Finally, substitute these values into the product rule formula and simplify to find the derivative of ( f(x) ).

( u' = e^x + 1 )

( v' = 2x - 1 )

Using the product rule formula:

( f'(x) = (e^x + x)(2x - 1) + (x^2 - x)(e^x + 1) )

( f'(x) = (2xe^x - e^x + 2x^2 - 2x) + (xe^x - xe^x + x^2 - x) )

( f'(x) = 2xe^x - e^x + 2x^2 - 2x + x^2 - x )

( f'(x) = 2xe^x - e^x + 3x^2 - 3x )

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 differentiate # f(x)=(2x+1)(4-x^2)(1+x^2) # using the product rule?
- What is the derivative of #sqrt(5x+sqrt(5x+sqrt(5x)))# ?
- How do you find the derivative of #y=2/(3x^2)#?
- How do you differentiate #f(x)=-3tan4x^2# using the chain rule?
- How do you find dy/dx by implicit differentiation for #2x^3 + x^2*y - xy^3 = 6#?

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