If \(y = x^{2}\cos x\), then \(\displaystyle\frac{dy}{dx}\) is equal to
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(2x\cos x - x^{2}\sin x\)
By the product rule:
\( \displaystyle \frac{dy}{dx} = \frac{d}{dx}(x^{2}) \cdot \cos x + x^{2} \cdot \frac{d}{dx}(\cos x) \)
\( = 2x\cos x - x^{2}\sin x \)