Question

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

Answer 1

`(d f(x))/(d x)=3*e^x* x^2+e^x*(x^3-1) *l n (e)`

Explanation:

`f(x)=e^x(x^3-1)`

`(d f(x))/(d x)=(e^x)'*(x^3-1)+(x^3-1)^'*e^x`

`(d f(x))/(d x)=e^x*l n e*(x^3-1)+3x^2*e^x`

`(d f(x))/(d x)=3*e^x* x^2+e^x*(x^3-1) *l n (e)`