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Question: If sec\(\left( \frac{x + y}{x - y} \right)\) = a, then \(\frac{dy}{dx}\) is...

If sec(x+yx−y)\left( \frac{x + y}{x - y} \right) = a, then dydx\frac{dy}{dx} is

A

x/y

B

y/x

C

y

D

x

Answer

y/x

Explanation

Solution

x + y / x – y = sec–1x

(x−y)(1+dy/dx)−(x+y)(1−dy/dx)(x−y)2\frac{(x - y)(1 + dy/dx) - (x + y)(1 - dy/dx)}{(x - y)^{2}}= 0

⇒ dydx=yx\frac{dy}{dx} = \frac{y}{x}