What is d/dx(√(x^2 + 1))?

Derivatives & Second-Order Derivatives · Question 17 of 96

Question 17

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What is $\frac{d}{dx}\left(\sqrt{x^{2} + 1}\right)$ ?

\frac{x}{\sqrt{x^{2} + 1}}

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\frac{1}{2 \sqrt{x^{2} + 1}}

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- \frac{x}{\sqrt{x^{2} + 1}}

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\frac{2 x}{\sqrt{x^{2} + 1}}

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CorrectNot quiteAnswer A

Correct answer: A

Use the chain rule: differentiate the outer function, then multiply by the derivative of what is inside it.
$\frac{d}{dx}\left(\sqrt{x^{2} + 1}\right) = \frac{x}{\sqrt{x^{2} + 1}}$ .

Worth noting

$\frac{1}{2 \sqrt{x^{2} + 1}}$ differentiates the outside only and drops the inside's derivative.

Ten questions from Derivatives & Second-Order Derivatives, at your own pace.

Ten questions from Derivatives & Second-Order Derivatives, at your own pace.