Question

How do you differentiate `f(x)=sqrt(1/csc(2/x )` using the chain rule?

Answer 1

`f'(x)=-csc(2/x)/(x^2*sqrt(sin(2/x)))`

Explanation:

Note that `csc(x)=1/sin(x)`
so we get by the chain rule

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