If \(y = \sin x\cos x\tan x\), where \(\cos x \ne 0\), then \(\displaystyle\frac{dy}{dx}\) is equal to
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\sin 2x\)
Since \(\tan x = \frac{\sin x}{\cos x}\), the product simplifies first:
\( \displaystyle y = \sin x \cos x \cdot \frac{\sin x}{\cos x} = \sin^{2}x \)
By the chain rule:
\( \displaystyle \frac{dy}{dx} = 2\sin x\cos x = \sin 2x \)