Differentiate this

1.	Differentiate this
Answer» Step-by-step EXPLANATION: LET $y = \sqrt{ \frac{1 - \tan(x) }{1 + \tan(x) } } \\$ $\implies \: y = \sqrt{ \frac{ \tan( \frac{\pi}{4} ) - \tan(x) }{1 + \tan( \frac{\pi}{4} ) . \tan(x) } } \\$ $\implies \: y = \sqrt{ \tan( \frac{\pi}{4} - x) } \\$ $\implies \: \frac{dy}{dx} = \frac{ - 1}{2 \sqrt{ \tan( \frac{\pi}{4} - x)} } . \frac{d}{dx} ( \tan( \frac{\pi}{4} - x) ) \\$ $\implies \: \frac{dy}{dx} = \frac{ - 1}{2 \sqrt{ \tan( \frac{\pi}{4} - x)} } . \sec^{2} ( \frac{\pi}{4} - x) \\$

Answer»

Step-by-step EXPLANATION:

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