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

If x^y = e^x–y, then dy/dx is:

$\frac{y}{1 + \log x}$

$\frac{x - y}{(1 + \log x)^{2}}$

$\frac{x - y}{1 + \log x}$

$\frac{\log x}{(1 + \log x)^{2}}$

Answer

$\frac{\log x}{(1 + \log x)^{2}}$

Explanation

x^y = e^x–y

y log x = (x – y) log e

y (1 + log x) = x

y = $\frac{x}{1 + \log x}$

$\frac{dy}{dx}$ = $\frac{(1 + \log x).1 - x\left( 0 + \frac{1}{x} \right)}{(1 + \log x)^{2}}$ = $\frac{\log x}{(1 + \log x)^{2}}$

Question: If x<sup>y</sup> = e<sup>x–y</sup>, then dy/dx is:...