5. continuity and differentiation — Maths STD 12 Science — Question

$\cos (x y)=-\sin x y$

diff. w.r.t. $x$

$-\sin x y\left[1 \cdot y+x \cdot \frac{d y}{d x}\right]=-\cos (x y)\left[1 \cdot y+x \cdot \frac{d y}{d x}\right]$

$y=\sin x+x \cdot \sin x y \cdot \frac{d y}{d x}=y \cdot \cos x y+x \cdot \cos x y \cdot \frac{d y}{d x}$

$(x \sin x y-x \cdot \cos x y) \frac{d y}{d x}=y \cos x y-y \sin x y$

$\frac{d y}{d x}=\frac{-y\left(\sin x y-\cos x y\right)}{x(\sin xy-\cos xy)}$

$\frac{d y}{d x}=-\frac{y}{x}$