The derivative of \(\sin^{2} x\) with respect to \(\cos x\), where \(\sin x \ne 0\), is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(-2\cos x\)
Let \(u = \sin^{2} x\) and \(v = \cos x\). The derivative of u with respect to v is \(\frac{du/dx}{dv/dx}\).
\( \displaystyle \frac{du}{dx} = 2\sin x\cos x, \quad \frac{dv}{dx} = -\sin x \)
\( \displaystyle \frac{du}{dv} = \frac{2\sin x\cos x}{-\sin x} = -2\cos x \)