Question

$\frac{d}{dx}\sqrt{(x\sin x)}=$

• A. $\frac{(\sin x+x\cos x)}{2\sqrt{(x\sin x)}}$
• B. $\frac{(\sin x+x\cos x)}{\sqrt{(x\sin x)}}$
• C. $\frac{(x\sin x+x\cos x)}{2\sqrt{(x\sin x)}}$
• D. $\frac{(x\sin x+x\cos x)}{\sqrt{(2x\sin x)}}$

Answer 1

The correct option is A

$\frac{(\sin x+x\cos x)}{2\sqrt{(x\sin x)}}$

Find the differentiation of given function:

Given, $y=\sqrt{(x\sin x)}$

Differentiate it with respect to $x$, we get

$\begin{array}{rcl}\therefore \frac{dy}{dx}& =& \left[\frac{1}{2\sqrt{(x\sin x)}}\right](x\cos x+\sin x)\\ & =& \frac{\mathbf{(}\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{}\mathbf{x}\mathbf{}\mathbf{+}\mathbf{}\mathbf{x}\mathbf{}\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{}\mathbf{x}\mathbf{}\mathbf{)}}{\mathbf{2}\sqrt{\mathbf{(}\mathbf{x}\mathbf{}\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{}\mathbf{x}\mathbf{)}}}\end{array}$

Hence, option (A) is correct.