Question

If $x\sin y=3\sin y+4\cos y$, then $\frac{dy}{dx}=$

• A. $\frac{-{\sin }^{2}y}{4}$
• B. $\frac{{\sin }^{2}y}{4}$
• C. $\frac{-{\cos }^{2}y}{4}$
• D. $\frac{{\cos }^{2}y}{4}$

Answer 1

The correct option is A $\frac{-{\sin }^{2}y}{4}$

Given $xsiny=3siny+4cosy$

$x\times cosy\times \frac{dy}{dx}+1\times \left(siny\right)=3\times cosy\frac{dy}{dx}+4\times (-siny)\frac{dy}{dx}$

$\frac{dy}{dx}[xcosy-3cosy+4siny]=-siny$

$\frac{dy}{dx}=\frac{-si{n}^{2}y}{4}$