If $3\sin \left(\mathrm{xy}\right)+4\cos \left(\mathrm{xy}\right)=5$ then $\frac{\mathrm{dy}}{\mathrm{dx}}=$

The given equation is $3\sin \left(\mathrm{xy}\right)+4\cos \left(\mathrm{xy}\right)=5$

Differentiate both sides 

$\begin{array}{rcl}\left[3\cos \left(xy\right)-4\sin \left(xy\right)\right]\left[x\frac{dy}{dx}+y\right]& =& 0\\ x\frac{dy}{dx}+y& =& 0\\ \frac{dy}{dx}& =& \boxed{\mathbf{-}\frac{\mathbf{y}}{\mathbf{x}}}\end{array}$