Question

How do you differentiate `f(x)=(x^2+x)(x^3-1)` using the product rule?

Answer 1

`d f(x)=(5x^4+4x^3-2x-1)*d x`

Explanation:

`f(x)=(x^2+x)(x^3-1)`

`d f(x)=((x^2+x)^' * (x^3-1)+(x^3-1)^' *(x^2+x))d x`

`d f(x)=[(2x+1)(x^3-1)+3x^2(x^2+x)]* d x`

`d f(x)=[2x^4-2x+x^3-1+3x^4+3x^3]*d x`

`d f(x)=(5x^4+4x^3-2x-1)*d x`