Question

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

• A. \N
• B. - 1
• C. 1
• D. 2

Answer 1

The correct option is B - 1

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