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Find the derivative of ln((1+cos(x))/(1-1cos(x)))

\frac{d}{dx}\left(\ln\left(\frac{1+\cos\left(x\right)}{1-\cos\left(x\right)}\right)\right)

Step by step solution

Problem

$\frac{d}{dx}\left(\ln\left(\frac{1+\cos\left(x\right)}{1-\cos\left(x\right)}\right)\right)$

Show full step-by-step solution

Answer

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

Main topic:

Differential calculus

Used formulas:

2. See formulas

Time to solve it:

0.44 seconds