x>1 માટે (2x)^ 2y =4e^ 2x-2y છે તો (1+log_e2x)^2dy dx =....... - Vidyadip

MCQ

$x>1$ માટે $(2x)^{2y}=4e^{2x-2y}$ છે તો $(1+log_e2x)^2\frac{dy}{dx}=.......$

A
$log_e2x$
B
$xlog_e2x$
C
$\frac{xlog_e2x+log_e2}{x}$
✓
$\frac{xlog_e2x-log2}{x}$

✓

Answer

Correct option: D.

$\frac{xlog_e2x-log2}{x}$

D

$2ylog2x=log4+2x-2y$

$2y(1+log2x)=log4+2x$

$y=\frac{(log2)+x}{1+log2x}$

$\frac{dy}{dx}=\frac{(1+log2x)(1)-(log2)+x)\frac{1}{x}}{(1+log2x)^2}$

$=\frac{log2x-\frac{log2}{x}}{(1+log2x)^2}$

$(1+log2x)^2\frac{dy}{dx}=log2x-\frac{log2}{x}$

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