Question

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

Answer 1

`f'(x)=csc(2x-x^3)cot(2x-x^3)(3x^2-2)`

Explanation:

Using the chain rule :

`f'(x) = d/dxcsc(2x-x^3)`

`= -csc(2x-x^3)cot(2x-x^3)(d/dx2x-x^3)`

`= -csc(2x-x^3)cot(2x-x^3)((d/dx2x)-(d/dxx^3))`

`= -csc(2x-x^3)cot(2x-x^3)(2-3x^2)`

`=csc(2x-x^3)cot(2x-x^3)(3x^2-2)`