Question

Find y}{dx} " align="absmiddle" class="latex-formula">
For this ☟
$y = cos(xy)$
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Answer 1

Answer:

$\frac{dy}{dx}=\frac{-y\sin xy}{1+\sin xy}$

Step-by-step explanation:

$\frac{dy}{dx}=-\frac{d}{dx} (xy) \sin(xy) \\ \\ =-\left(x \frac{dy}{dx}+y \right) \sin(xy) \\ \\ =-x \frac{dy}{dx} \sin(xy)-y\sin(xy) \\ \\ \frac{dy}{dx}(1+x\sin(xy))=-y \sin xy \\ \\ \frac{dy}{dx}=\frac{-y\sin xy}{1+\sin xy}$