Question

If $2^x-2^y=2^{x+y}$ then $\frac{dy}{dx}=$

• A. $2^{y-x}$
• B. $2^{y/x}$
• C. $-2^{y/x}$
• D. $2^{x/y}$

Answer 1

The correct option is A $2^{y-x}$

since $2^x-2^y=2^{x+y}$

hence $2^x-2^{x+y}=2^y$

and $2^y+2^{x+y}=2^x$

replace this in above we get

$\frac{dy}{dx}=\frac{2^y}{2^x}$

$\frac{dy}{dx}=2^{y-x}$

hence this is the answer