Question

derivative of log under root 1+xcosx/1-xcosx

Answer 1

Step-by-step explanation:

Let

$y = log \sqrt{ \frac{ 1 + x \cos(x) }{1 - x \cos(x) } }$

$\implies \: y = \frac{1}{2} log \frac{ 1 + x \cos(x) }{1 - x \cos(x) }$

$\implies \: y = \frac{1}{2} log \{ 1 + x \cos(x) \} - \frac{1}{2 }log \{ 1 - x \cos(x) \}$

$\implies \: \frac{dy}{dx} = \frac{ \cos(x) - x \sin(x) }{2(1 + x \cos(x) )} - \frac{x \sin(x) - \cos(x) }{2( 1 - x \cos(x) )}$