What is the derivative of this function  (1-sin(x))^(-1/2)?

Aug 19, 2016

$\cos \frac{x}{2 {\left(1 - \sin x\right)}^{\frac{3}{2}}}$

Explanation:

$f \left(x\right) = {\left(1 - \sin x\right)}^{- \frac{1}{2}}$

$f ' \left(x\right) = - \frac{1}{2} {\left(1 - \sin x\right)}^{- \frac{3}{2}} \cdot \frac{d}{\mathrm{dx}} \left(1 - \sin x\right)$ (Power rule and Chain rule)

$f ' \left(x\right) = - \frac{1}{2} {\left(1 - \sin x\right)}^{- \frac{3}{2}} \cdot \left(0 - \cos x\right)$

$f ' \left(x\right) = \cos \frac{x}{2 {\left(1 - \sin x\right)}^{\frac{3}{2}}}$