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Chain Rule of Differentiation

Differentiate...

Question

Differentiate $y = \sqrt{1 + x^{2}}$ w.r.t $x$

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Solution

$y = \sqrt{1 + x^{2}}$
$y^{2} = 1 + x^{2}$
$\Rightarrow 2 y \frac{d y}{d x} = 2 x$
$\Rightarrow \frac{d y}{d x} = \frac{x}{y}$
$∴ \frac{d y}{d x} = \frac{x}{\sqrt{1 + x^{2}}}$

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