Question

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

Answer 1

`f'(x)=(cosx+x)(9x^2-e^x)+(3x^3-e^x)(-sinx+1)`

Explanation:

Let `f=cosx+x and g=3x^3-e^x`

Then `f'=-sinx+1 and g'=9x^2-e^x`

Product Rule:
`f'(x)=fg'+gf'`

`f'(x)=(cosx+x)(9x^2-e^x)+(3x^3-e^x)(-sinx+1)`