Question

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

Answer 1

`f'(x) = 5x^4 + 3x^2 + 2x`

Explanation:

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

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

`f'(x) = 2x^4+2x +3x^4+3x^2`

`f'(x) = 5x^4 + 3x^2 + 2x`