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Chain Rule of Differentiation

If y=√1+x2 ...

Question

If $y = \sqrt{1 + x^{2}}$ Find $\frac{d y}{d x}$

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Solution

$y = \sqrt{1 + x^{2}} \frac{d y}{d x} = \frac{d}{d x} \sqrt{(1 + x^{2})} \frac{d y}{d x} = \frac{1}{2 \sqrt{1 + x^{2}}} \frac{d}{d x} (1 + x^{2}) \frac{d}{d x} = \frac{x}{\sqrt{1 + x^{2}}}$

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