Question

If $\cos \left(xy\right)=x$, then $\frac{dy}{dx}$ is equal to?

• A. $\frac{y+cosec\left(xy\right)}{x}$
• B. $\frac{y+\sin \left(xy\right)}{x}$
• C. $\frac{y+\cos \left(xy\right)}{x}$
• D. $-\frac{y+cosec\left(xy\right)}{x}$

Answer 1

The correct option is D $-\frac{y+cosec\left(xy\right)}{x}$

cos(xy)=x

Differentiating with respect to x :-

$\Rightarrow -sin\left(xy\right).[y+x\frac{dy}{dx}]=1$

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

$\Rightarrow x\frac{dy}{dx}=-[\frac{1}{sinxy}+y]$

$\Rightarrow \frac{dy}{dx}=\frac{-1}{x}\left[\frac{1}{sinxy+y}\right]=-\frac{(y+cosecxy)}{x}$