If x ^ y =2^ x - y , then d y d x = ________ - Vidyadip

MCQ

If $x ^{ y }=2^{ x - y }$, then $\frac{ d y}{ d x}=$ ________

A
$\frac{x \log 2-y}{x \log 2 x}$
✓
$\frac{x \log 2+y}{x \log 2 x}$
C
$\frac{x \log 2+x}{y \log 2 x}$
D
$\frac{y \log 2-x}{x \log 2 x}$

✓

Answer

Correct option: B.

$\frac{x \log 2+y}{x \log 2 x}$

If $x^y=2^{x-y}$, then $\frac{d y}{d x}=\frac{ x \log 2+ y }{ x \log 2 x }$

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