Q. 65 Find the derivatives of each of ... [FREE SOLUTION]

91影视

Chapter 2: Q. 65 (page 198)

Find the derivatives of each of the absolute value and piecewise-defined functions in Exercises 65-72.
$f (x) = |x|$

Short Answer

Expert verified

The derivative of the function is $f' (x) = \{\begin{cases} - 1 x < 0 \\ D N E x = 0 \\ 1 x > 0 \end{cases}$ .

Step by step solution

Step 1. Given Information

The given function is $f (x) = |x|$ .

Step 2. Rewrite the function

The given function can be rewritten as,

$f (x) = \{\begin{cases} - x x 鈮� 0 \\ x x > 0 \end{cases}$

Step 3. Find the derivative

It is known that, the derivative of the identity function is $\frac{d}{d x} (x) = 1$ .
Find the derivative for localid="1648725381209" $x < 0$ .

$\begin{array}{rcl} f' (x) & = & \frac{d}{d x} (- x) \\ = & - 1 \end{array}$

Find the derivative for $x > 0$ .

$\begin{array}{rcl} f' (x) & = & \frac{d}{d x} (x) \\ = & 1 \end{array}$

Since $- 1 鈮� 1$ , the derivatives at left and right pieces are not equal at $x = 0$ . The derivative does not exists at $x = 0$ .
So, the derivative of the function is, $f' (x) = \{\begin{cases} - 1 x < 0 \\ D N E x = 0 \\ 1 x > 0 \end{cases}$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Find the derivatives of each of the absolute value and piecewise-defined functions in Exercises 65-72.
$f (x) = |x|$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Rewrite the function

Step 3. Find the derivative

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Decision Maths

Statistics

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

91影视

Find the derivatives of each of the absolute value and piecewise-defined functions in Exercises 65-72.f(x)=x

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Rewrite the function

Step 3. Find the derivative

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Decision Maths

Statistics

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Find the derivatives of each of the absolute value and piecewise-defined functions in Exercises 65-72.
$f (x) = |x|$