Question

How do you differentiate `f(x)=csc(5x^5)`?

Answer 1

Use the chain rule and derivative of cosecant.

Explanation:

`d/dx(cscx) = -cscxcotx` `" "` (Memorize this)

So `d/dx(cscu) = -cscucotu (du)/dx`

`f(x) = csc(5x^5)`

`f'(x) = -csc(5x^5)cot(5x^5) d/dx(5x^5)`

`= -csc(5x^5)cot(5x^5) * (25x^4)`

`= -25x^4 csc(5x^5)cot(5x^5)`