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Find the derivative of ((cos(x)-1)/(sin(x)))^(1/2)

\frac{d}{dx}\left(\left(\frac{\cos\left(x\right)-1}{\sin\left(x\right)}\right)^{\frac{1}{2}}\right)

Step by step solution

Problem

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

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Answer

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

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

Main topic:

Differential calculus

Used formulas:

3. See formulas

Time to solve it:

0.32 seconds