If x=e^ ( xy ), then dy dx=

Correct answer: B. (b) : We have, x=e^x/y By taking log on both sides, we get log ⁡x= log ⁡e^x/y log ⁡x= xy or y log ⁡x=x Differentiating w.r.t x, dy dx log ⁡x+ yx=1 ⇒ dy dx= 1- yx log ⁡x= x-yx log ⁡x

JEE Previous Year Question

$If x = e^{(\frac{x}{y})}, then \frac{dy}{dx} =$

Topic: JEE PYQ

Answer: B. Full step-by-step solution below.

A $\frac{x - y}{x log y}$
B $\frac{x - y}{x log x}$
C $\frac{x - y}{y log x}$
D $\frac{x + y}{x log x}$

Correct answer: B

Solution

(b) : We have, x = e^{x / y} By taking log on both sides, we get log x = log e^{x / y} log x = \frac{x}{y} or y log x = x Differentiating w.r.t x, \frac{dy}{dx} log x + \frac{y}{x} = 1 \Rightarrow \frac{dy}{dx} = \frac{1 - \frac{y}{x}}{log x} = \frac{x - y}{x log x}

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