# How do you differentiate #f(x)=e^x(x^3-1) # using the product rule?

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

To differentiate ( f(x) = e^x(x^3 - 1) ) using the product rule, follow these steps:

- Identify the two functions being multiplied: ( u(x) = e^x ) and ( v(x) = x^3 - 1 ).
- Use the product rule formula: ( f'(x) = u'(x)v(x) + u(x)v'(x) ).
- Find the derivatives of ( u(x) ) and ( v(x) ):
- ( u'(x) = e^x ) (derivative of ( e^x ) is itself).
- ( v'(x) = 3x^2 ) (derivative of ( x^3 - 1 ) is ( 3x^2 )).

- Substitute the derivatives and original functions into the product rule formula:
- ( f'(x) = e^x(x^3 - 1) + e^x(3x^2) ).

- Simplify the expression if necessary:
- ( f'(x) = e^x(x^3 - 1 + 3x^2) ).
- ( f'(x) = e^x(x^3 + 3x^2 - 1) ).

So, the derivative of ( f(x) = e^x(x^3 - 1) ) using the product rule is ( f'(x) = e^x(x^3 + 3x^2 - 1) ).

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.

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