If y = x sin x, find δ y/δ x

Correct Answer is : sin x + x cos x

Correct Answer is : sin x + x cos x

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JAMB Mathematics 2013 Paper

Question : 20

Total: 47

\frac{\delta y}{\delta x}

Solution:

Concept:

The function is a product of two differentiable functions, so use the product rule for differentiation.

Explanation:

Let

u = x

and

v = \sin x

Then

\frac{du}{dx} = 1

and

\frac{dv}{dx} = \cos x

By the product rule,

\frac{dy}{dx} = u\frac{dv}{dx} + v\frac{du}{dx}

Substitute the values:

\frac{dy}{dx} = x(\cos x) + (\sin x)(1)

Simplify:

\frac{dy}{dx} = x\cos x + \sin x

This matches option D.

Answer:

\sin x + x\cos x

(Option D)

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