Question

If $2^x+2^y=2^{x+y}$, then the value of $\frac{dy}{dx}$ at x = y = 1 is

• A. -1
• B. 1
• C. 2

Answer 1

The correct option is A -1

$2^x+2^y=2^{x+y}$
$\therefore 2^x.lo{g}_{e}2+2^y.lo{g}_{e}2\frac{dy}{dx}$
$=2^{x+y}.lo{g}_{e}2(1+\frac{dy}{dx})or{2}^x+2^y\frac{dy}{dx}=2^{x+y}(1+\frac{dy}{dx})\therefore \frac{dy}{dx}=\frac{2^{x+y}-2^x}{2^y-2^{x+y}}\frac{dy}{dx}{|}_{x=y=1}=-1$