If xy = ex – y, then dy/dx is equal to | MATH - DIFFERENTIATION OF IMPLICIT FUNCTION, PARAMETRIC AND COMPOSITE FUNCTIONS | SolveeIt | Solveeit

Today, August 18

Question

If x^y = e^{x – y}, then dy/dx is equal to

A

(1 + log x)^–1

B

( 1 + log x)^–2

C

(log x) [1 + log x]^–2

D

None of these

Answer

(log x) $1 + log x$ ^–2

Explanation

Solution

x^y = e^x–y

y log_ex = x – y

y = $\frac{x}{1 + \log_{e}x}$ = $\frac{dy}{dx} = \frac{\log_{e}x}{(1 + \log_{e}x)^{2}}$