Question

$y = \sqrt{x { }^{2} + 1}$
Differentiation....
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Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Use Chain Rule on $\sf\frac{d}{dx} \sqrt{{x}^{2}+1}$. Let $\sf u={x}^{2}+1$. Since $\sf\sqrt{u}={u}^{\frac{1}{2}}$ , using the Power Rule, $\sf\frac{d}{du} {u}^{\frac{1}{2}}=\frac{1}{2}{u}^{-\frac{1}{2}}$

$\tt \red{ \implies \dfrac{1}{2\sqrt{{x}^{2}+1}}(\dfrac{d}{dx} {x}^{2}+1)}$

Use Power Rule: $\sf\frac{d}{dx} {x}^{n}=n{x}^{n-1}$

$\tt \pink{ \implies\dfrac{x}{\sqrt{{x}^{2}+1}}}$