Question

Differentiate the above question
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Answer 1

Answer:

Formula used :

$\longmapsto\sec {}^{ - 1} ( \theta) = \cos {}^{ - 1} ( \frac{1}{ \theta} ) \\ \longmapsto\cos {}^{ - 1} ( \theta) + \sin {}^{ - 1} ( \theta) = \frac{\pi}{2}\\ \longmapsto \frac{d(c)}{dx}=0,\: where\:c\: is\: a\: constant$

Now,

$y= \sec {}^{ - 1} ( \frac{x + 1}{x - 1} ) + \sin {}^{ - 1} ( \frac{x - 1}{x + 1} ) \\ y= \cos {}^{ - 1} ( \frac{x - 1}{x + 1} ) + \sin {}^{ - 1} ( \frac{x - 1}{x + 1} ) \\ y= \boxed{\frac{\pi}{2} }\\ \boxed{\frac{dy}{dx}=0}$

• dy/dx = 0 is the right answer.