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Solved Example
Solution:
Given: $x\sin x$
$\frac{dy}{dx}$ = $\frac{d}{dx} (x\sin x)$
= $x\frac{d}{dx}(\sin x)$ + $\sin x \frac{d}{dx} (x)$
= $x\cos x + \sin x$
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Solved Examples
Solution:
Given y = $e^{x}\log x$
$\frac{dy}{dx}$ = $e^{x}$$\frac{d}{dx}$$(\log x)$ + $\log x$ $\frac{d}{dx}$$(e^{x})$
$\frac{dy}{dx}$ = $\frac{e^{x}}{x}$ + $\log x e^{x}$
Solution:
Given y = $x^{2} \sin^{-1} x$
$\frac{dy}{dx}$ = $x^{2}$$\frac{d}{dx}$$(\sin^{-1}x)$ + $\sin^{-1}$$\frac{d}{dx}$(x^{2})$
= $\frac{x^{2}}{\sqrt{1-x^{2}}}$ + $\sin^{-1}x$(2x)