Question

If sin${}^2$ x + cos${}^2$ y = 1 find $\frac{dy}{dx}$

Answer 1

${\sin }^{2}x+{\cos }^{2}y=1$

$\frac{d}{dx}({\sin }^{2}x+{\cos }^{2}y)=\frac{d}{dx}\left(1\right)$

$2\sin x\cos x-2\sin y\cos y\frac{dy}{dx}=0$

$\sin 2x=\sin 2y\frac{dy}{dx}$

$\frac{dy}{dx}=\frac{\sin 2x}{\sin 2y}$