Question

How do you differentiate `f(x)=-x^3*(-5x)` using the product rule?

Answer 1

`20x^3`

Explanation:

The product rule states that the derivative of a product of two functions is the first function times the derivative of the second, plus the second function times the derivative e of the first.
ie. `d/dx[f(x)*g(x)]=f(x)*g'(x)+g(x)*f'(x)`.

Application in this particular case yields

`f'(x)=-x^3(-5)+(-5x)(-3x^2)`

`=5x^3+15x^3`

`=20x^3`