Answered: Let fi=al tor 0, then (x) is Teictone…

Math

Calculus

Let fi=al tor 0, then (x) is Teictone A- CNonel thene ONt arfieed

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.4: The Singular Value Decomposition

Problem 53EQ

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Question

Let fi=al tor 0, then (x) is
Teictone
A-
CNonel thene
ONt arfieed

Expert Solution

Step 1

Given that

f(x)=|x|.

Step 2

To find f'(x).

Rewrite the function f(x)=|x| as $|x| = \sqrt{x^{2}}$

Now to find the derivative of $\sqrt{x^{2}}$ .

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

But $|x| = \sqrt{x^{2}}$

Thus $\frac{d}{d x} (|x|) = \frac{x}{|x|}$ .

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