Q. 68 We have to find the function of ... [FREE SOLUTION]

Chapter 2: Q. 68 (page 234)

We have to find the function of given derivative
$f^{鈥�} (x) = \frac{1}{1 + 9 x^{2}}$

Short Answer

Expert verified

The given function is the answer of given derivative

f (x) = \frac{1}{3} \tan^{鈭� 1} 鈦� 3 x

Step by step solution

Step 1.Given information

We have been given the derivative function

f^{鈥�} (x) = \frac{1}{1 + 9 x^{2}}

Step 2.Finding the approximate function of derivative

One can think of $\tan^{鈭� 1} 鈦� x$ as the denominator is suggesting about this function

\begin{aligned} f (x) = \tan^{鈭� 1} 鈦� 3 x \\ f (x) = \tan^{鈭� 1} 鈦� 3 x \\ f^{鈥�} (x) = \frac{1}{1 + (3 x)^{2}} \frac{d}{d x} (3 x) \\ = \frac{3}{1 + 9 x^{2}} \end{aligned}

Step 3.Finding more appropriate function

$f (x) = \frac{1}{3} \tan^{- 1} (3 x^{})$

Here we have used product rule

$\begin{aligned} f (x) = \frac{1}{3} \tan^{鈭� 1} 鈦� 3 x \\ f^{鈥�} (x) = \frac{1}{3} (\frac{1}{1 + (3 x)^{2}} \frac{d}{d x} (3 x)) \\ = \frac{1}{3} (\frac{3}{1 + 9 x^{2}}) \\ = \frac{1}{1 + 9 x^{2}} \end{aligned}$

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

We have to find the function of given derivative
$f^{鈥�} (x) = \frac{1}{1 + 9 x^{2}}$

Short Answer

Step by step solution

Step 1.Given information

Step 2.Finding the approximate function of derivative

Step 3.Finding more appropriate function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Theoretical and Mathematical Physics

Discrete Mathematics

Logic and Functions

Probability and Statistics

Study anywhere. Anytime. Across all devices.

91影视

We have to find the function of given derivativef鈥�(x)=11+9x2

Short Answer

Step by step solution

Step 1.Given information

Step 2.Finding the approximate function of derivative

Step 3.Finding more appropriate function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Theoretical and Mathematical Physics

Discrete Mathematics

Logic and Functions

Probability and Statistics

Study anywhere. Anytime. Across all devices.

We have to find the function of given derivative
$f^{鈥�} (x) = \frac{1}{1 + 9 x^{2}}$