Question

How do you find the derivative for `(3x+1)^4(2x-3)^3`?

Answer 1

`f'(x)=6(3x+1)^3(2x-3)^2 (6x-5)`

Explanation:

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

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

`f'(x)=(3x+1)^3(2x-3)^2 (12(2x-3)+6(3x+1))`

`f'(x)=(3x+1)^3(2x-3)^2 (42x-30)`

`f'(x)=6(3x+1)^3(2x-3)^2 (6x-5)`