Question

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

Answer 1

`f'(x)=4(3x^2-2x)sec^4(x^3-x^2)tan(x^3-x^2)`

Explanation:

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

`f'(x)=4(sec(x^3-x^2))^3*sec(x^3-x^2))tan(x^3-x^2)*(3x^2-2x)`

`f'(x)=4(3x^2-2x)sec^4(x^3-x^2)tan(x^3-x^2)`