Question

How do you differentiate `f(x) = x^3(2x-5)^4` using the chain rule?

Answer 1

`f'(x)=x^2(2x-5)^3(14x-15)`

Explanation:

`f(x)=x^3(2x-5)^4`

`f'(x)=x^3times4(2x-5)^3times2+(2x-5)^4times3x^2`

`f'(x)=(2x-5)^3(8x^3+6x^3-15x^2)`

`f'(x)=(2x-5)^3(14x^3-15x^2)`

`f'(x)=x^2(2x-5)^3(14x-15)`