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

Mar 4, 2016

$f ' \left(x\right) = \frac{1}{2 \sqrt{\csc \left(\frac{2}{x}\right)}} \cdot - \csc \left(\frac{2}{x}\right) \cot \left(\frac{2}{x}\right) \left(- \frac{2}{x} ^ 2\right)$

Explanation:

First take the derivative of sqrt(exponent of 1/2) while keeping everything else inside the same next take the derivative of csc while keeping (2/x) the same and finally the derivative of (2/x)