Question

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

Answer 1

`f'(x)=3(x^2+1)(x-3)+6x(x-3)^2`

Explanation:

The product rule sates that `d/dx[f(x)*g(x)]=f(x)*g'(x)+g(x)*f'(x)`

Thus in the given example, we need the power rule for the second factor, and get

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