Question

How do you differentiate `f(x)=x^2 (4x^3 - 1)` using the product rule?

Answer 1

`f'(x)=x(11x^3-2)`

Explanation:

According to the product rule:

`f'(x)=(4x^3-1)color(blue)(d/dx[x^2])+x^2color(red)(d/dx[4x^3-1])`

Find each derivative.

`f'(x)=2x(4x^3-1)+x^2(3x^2)`

`f'(x)=8x^4-2x+3x^4`

`f'(x)=x(11x^3-2)`