Question

answer this question fast​

Answer 1

Answer:

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

Step-by-step explanation:

Given that,  $e^{-xy} -4xy =0$

             =>   $e^{-xy}=-4xy$

             =>   $-xy = log_{e}(-4xy)$

             =>   $\frac{d}{dx} (-xy)=\frac{d}{dx}(log_{e}(-4 x y ))$

             =>   $-(y+x\frac{dy}{dx}) = \frac{1}{-4xy}(-4)(y+x\frac{dy}{dx})$

             =>   $xy+1=0$

             =>   $\frac{d}{dx}(xy+1)=0$

             =>   $x\frac{dy}{dx}+y =0$

             =>   $\frac{dy}{dx}=-\frac{y}{x }$