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

Nov 1, 2016

f'(x)=(csc^2(1/sqrtx))/(2x^(3/2)
$f \left(x\right) = \cot \left(\frac{1}{\sqrt{x}}\right) = \cot \left(\frac{1}{x} ^ \left(\frac{1}{2}\right)\right) = \cot \left({x}^{- \frac{1}{2}}\right)$
$f ' \left(x\right) = - {\csc}^{2} \left(\frac{1}{\sqrt{x}}\right) \cdot - \frac{1}{2} {x}^{- \frac{3}{2}}$
f'(x)=(csc^2(1/sqrtx))/(2x^(3/2)