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JAMB Mathematics 2017 Paper

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Question : 7

Total: 44

If y = x Sin x, find

\frac{dy}{dx}

\frac{\pi}{2}

$\frac{-\pi}{2}$
-1
1
$\frac{\pi}{2}$

Solution:

Concept:

Use the product rule to differentiate

y = x\sin x

.

Explanation:

Given

y = x\sin x

, apply the product rule:

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

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

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

Now substitute

x = \frac{\pi}{2}

:

\frac{dy}{dx} = \sin\frac{\pi}{2} + \frac{\pi}{2}\cos\frac{\pi}{2}

\sin\frac{\pi}{2} = 1

and

\cos\frac{\pi}{2} = 0

\frac{dy}{dx} = 1 + \frac{\pi}{2}(0) = 1

Answer:

1

Option C.

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