Q. 77 In Exercises 72鈥�77, find a fun... [FREE SOLUTION]

Chapter 2: Q. 77 (page 234)

In Exercises 72鈥�77, find a function f that has the given derivative f. In each case you can find the answer with an educated guess-and-check process. (Some of these exercises involve hyperbolic functions.)
$f' (x) = \frac{3}{\sqrt{4 + 9 x^{2}}}$

Short Answer

Expert verified

The function that has the derivative $f' (x) = \frac{3}{\sqrt{4 + 9 x^{2}}}$ is $f (x) = \sin h^{- 1} (\frac{3 x}{2})$ .

Step by step solution

Step 1. Given Information.

The derivative:

$f' (x) = \frac{3}{\sqrt{4 + 9 x^{2}}}$

Step 2. Guess the formula for the given derivative.

We know that,

$\frac{d}{d x} (\sin h^{- 1} (x)) = \frac{1}{\sqrt{1 + x^{2}}}$

So we can conclude that the derivative will be of the form of sinefunction.

Step 3. Check guess-and-check process.

Consider

$f (x) = \sin h^{- 1} (3 x) f' (x) = \frac{1}{\sqrt{1 + 9 x^{2}}} . 3 = \frac{3}{\sqrt{1 + 9 x^{2}}}$

which is not a given derivative.

Step 4. Check another function.

Consider the function,

$f (x) = \sin h^{- 1} (\frac{3 x}{2}) f' (x) = \frac{1}{\sqrt{1 + {(\frac{3 x}{2})}^{2}}} . \frac{3}{2} = \frac{1}{\sqrt{1 + \frac{9 x^{2}}{4}}} . \frac{3}{2} = \frac{2}{\sqrt{4 + 9 x^{2}}} . \frac{3}{2} = \frac{3}{\sqrt{4 + 9 x^{2}}}$

which is a given derivative.

So the function is $f (x) = \sin h^{- 1} (\frac{3 x}{2})$

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

In Exercises 72鈥�77, find a function f that has the given derivative f. In each case you can find the answer with an educated guess-and-check process. (Some of these exercises involve hyperbolic functions.)
$f' (x) = \frac{3}{\sqrt{4 + 9 x^{2}}}$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Guess the formula for the given derivative.

Step 3. Check guess-and-check process.

Step 4. Check another function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Calculus

Pure Maths

Applied Mathematics

Mechanics Maths

Statistics

Study anywhere. Anytime. Across all devices.

91影视

In Exercises 72鈥�77, find a function f that has the given derivative f. In each case you can find the answer with an educated guess-and-check process. (Some of these exercises involve hyperbolic functions.)f'(x)=34+9x2

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Guess the formula for the given derivative.

Step 3. Check guess-and-check process.

Step 4. Check another function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Calculus

Pure Maths

Applied Mathematics

Mechanics Maths

Statistics

Study anywhere. Anytime. Across all devices.

In Exercises 72鈥�77, find a function f that has the given derivative f. In each case you can find the answer with an educated guess-and-check process. (Some of these exercises involve hyperbolic functions.)
$f' (x) = \frac{3}{\sqrt{4 + 9 x^{2}}}$