First slide

Diffrentiation

Question

$If y = x^{2} \sin x, then \frac{d y}{d x} will be$

Moderate

A

$x^{2} \cos x + 2 x \sin x$
B

$2 x \sin x$
C

$x^{2} \cos x$
D

$2 x \cos x$

Solution

$\begin{array}{l} y = x^{2} \sin x \\ \frac{d y}{d x} = \frac{d}{d x} (x^{2} \sin x) \\ = x^{2} \frac{d \sin x}{d x} + \sin x \frac{d x^{2}}{d x} [∵ \frac{d}{d x} (u v) = u \frac{d v}{d x} + v \frac{d v}{d x}] \\ = x^{2} [\cos x] + \sin x [2 x] (∵ \frac{d}{d x} \sin x = \cos x, \frac{d x^{n}}{d x} = n x^{n - 1}) \\ = x^{2} \cos x + 2 x \sin x \end{array}$

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