Question

If $\sin \left(xy\right)+\cos \left(xy\right)=0$ then $\frac{dy}{dx}=$

• A. $\frac{y}{x}$
• B. $-\frac{y}{x}$
• C. $-\frac{x}{y}$
• D. $\frac{x}{y}$

Answer 1

Answer: (B)

$-\frac{y}{x}$

$\cos xy(x{y}^{\prime }+y)-\sin xy(x{y}^{\prime }+y)=0$

$(x{y}^{\prime }+y)(\cos xy-\sin xy)=0$

$So,y^{\prime }=\frac{-y}{x}$ (Since, $\sin xy\ne \cos xy$ )