Correct Answer - Option 4 : (x
2 + 2) cos x
Concept:
Derivatives:
Product rule:
For two functions u and v of x, we have:
\(\rm \frac{d}{dx}uv=\frac{du}{dx}v+u\frac{dv}{dx}\)
\(\rm \frac{d}{dx}x^n=nx^{n-1}\)
Calculation:
Using the product rule of derivatives, we get:
\(\rm \frac{dy}{dx}\) = \(\rm \frac{d}{dx} \left(2x \cos x + x^2 \sin x\right)\)
= (2 cos x - 2x sin x) + (2x sin x + x2 cos x)
= 2 cos x + x2 cos x
= (x2 + 2) cos x