Chapter 2: Q. 25 (page 210)

Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
$f (x) = \frac{1}{\sqrt{x^{2} + 1}}$

Short Answer

Expert verified

The required answer is $- \frac{x}{{(x^{2} + 1)}^{\frac{3}{2}}}$

Step by step solution

Step 1. Given Information

The given function is $f (x) = \frac{1}{\sqrt{x^{2} + 1}}$

Step 2. Calculation

Differentiate both the sides with respect to x, we get,

$f' (x) = \frac{d}{d x} {(x^{2} + 1)}^{- \frac{1}{2}} = - \frac{1}{2} {(x^{2} + 1)}^{- \frac{1}{2} - 1} \frac{d}{d x} (x^{2} + 1) = - \frac{1}{2} {(x^{2} + 1)}^{- \frac{3}{2}} (\frac{d}{d x} (x^{2}) + \frac{d}{d x} (1)) = - \frac{1}{2} {(x^{2} + 1)}^{- \frac{3}{2}} (2 x) = - \frac{x}{{(x^{2} + 1)}^{\frac{3}{2}}}$

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Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
$f (x) = \frac{1}{\sqrt{x^{2} + 1}}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

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Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating. f(x)=1x2+1

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
$f (x) = \frac{1}{\sqrt{x^{2} + 1}}$