Q. If $\sec\left( \frac{x - y}{x + y} \right)\ = a,\ then\frac{dy}{dx}\$is
A) $\frac{y}{x}$
B) $- \frac{y}{x}$
C) $\frac{x}{y}$
D) $- \frac{x}{y}$
Explanation
(a)
Since, $\frac{x - y}{x + y} = \sec^{- 1}a$
$\Rightarrow \ \frac{(x + y)\left( 1 - \frac{dy}{dx} \right) - (x - y)\left( 1 + \frac{dy}{dx} \right)}{(x + y)^{2}}$=0
$\Rightarrow x + y - x + y - (x + y + x - y)\frac{dy}{dx} = 0 \Rightarrow \frac{dy}{dx} = \frac{y}{x}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.