Question

Differentiate ${\sin }^{2}x$ with respect to $e^{\cos x}$.

Answer 1

$y_1={\sin }^{2}x$

$y_2=e^{\cos x}$

$\frac{d{y}_1}{d{y}_2}=\frac{d{y}_1}{dx}.\frac{dx}{d{y}_2}$

$=\frac{2\sin x\cos x}{e^{\cos x}.(-\sin x)}$

$=\frac{-2\cos x}{e^{\cos x}}$