Question

differentiate y = √sinx with respect to x

Answer 1

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$y = {\sqrt{Sin\: x}}$

Differentiate on both sides with respect to x

$\frac{dy}{dx} = \frac{d}{dx} {\sqrt{Sin\: x}}$

= $\frac{1}{2\sqrt{Sin\: x}} × \frac{d}{dx}{Sin\: x}$

= $\frac{1}{2\sqrt{Sin\: x}} × Cos\: x$

=$\frac{Cos\: x}{2\sqrt{Sin\: x}}$

Since, we have,
$\frac{d}{dx}\sqrt{x}= \frac{1}{2\sqrt{x}}$

$\frac{d}{dx}Sin\: x = Cos\: x$