Question

Calcule a derivada

y=(2x-y)e^xy

Answer 1

$y=(2x-y)e^{xy}$
$\displaystyle \frac{dy}{dx}=\frac{d}{dx}(2x-y)e^{xy}\\\\i)~~~~\frac{dy}{dx}=\frac{d}{dx}(2x-y)\cdot e^{xy}+\frac{d}{dx}e^{xy}(2x-y)\\\\ii)~~~y'=(2-y')e^{xy}+\left(\frac{d}{du}e^u\cdot \frac{du}{dx}\right)(2x-y)\\\\\\~~~~~~~u=xy\implies \frac{du}{dx}=y+xy'\\\\\\iii)~~y'=(2-y')e^{xy}+e^{xy}(y+xy')(2x-y)\\\\iv)~~y'=e^{xy}(2-y'+xy')=\frac{dy}{dx}$