Question

How do you differentiate `f(x)=cot(1/sqrt(x))` using the chain rule?

Answer 1

`f'(x)=(csc^2(1/sqrtx))/(2x^(3/2)`

Explanation:

`f(x)=cot(1/sqrtx)=cot(1/x^(1/2))=cot(x^(-1/2))`

`f'(x)=-csc^2(1/sqrtx)*-1/2 x^(-3/2)`

`f'(x)=(csc^2(1/sqrtx))/(2x^(3/2)`