Question

differentiate this ​

Answer 1

Step-by-step explanation:

Let

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

$\implies \: y = \sqrt{ \frac{ \tan( \frac{\pi}{4} ) - \tan(x) }{1 + \tan( \frac{\pi}{4} ) . \tan(x) } }$

$\implies \: y = \sqrt{ \tan( \frac{\pi}{4} - x) }$

$\implies \: \frac{dy}{dx} = \frac{ - 1}{2 \sqrt{ \tan( \frac{\pi}{4} - x)} } . \frac{d}{dx} ( \tan( \frac{\pi}{4} - x) )$

$\implies \: \frac{dy}{dx} = \frac{ - 1}{2 \sqrt{ \tan( \frac{\pi}{4} - x)} } . \sec^{2} ( \frac{\pi}{4} - x)$