Q. 46 Find the derivatives of the func... [FREE SOLUTION]

91影视

Chapter 2: Q. 46 (page 210)

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

Short Answer

Expert verified

The required answer is $- \frac{1}{4 \sqrt{1 + \sqrt{1 + \sqrt{1 - 2 x}}} \sqrt{1 + \sqrt{1 - 2 x}} \sqrt{1 - 2 x}}$

Step by step solution

Step 1. Given Information

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

Step 2. Calculation

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

$f' (x) = \frac{d}{d x} {(1 + \sqrt{1 + \sqrt{1 - 2 x}})}^{\frac{1}{2}} = \frac{1}{2} {(1 + \sqrt{1 + \sqrt{1 - 2 x}})}^{\frac{1}{2} - 1} \frac{d}{d x} (1 + \sqrt{1 + \sqrt{1 - 2 x}}) = \frac{1}{2} {(1 + \sqrt{1 + \sqrt{1 - 2 x}})}^{\frac{- 1}{2}} \frac{d}{d x} {(1 + \sqrt{1 - 2 x})}^{\frac{1}{2}} = \frac{1}{2} {(1 + \sqrt{1 + \sqrt{1 - 2 x}})}^{\frac{- 1}{2}} (\frac{1}{2} {(1 + \sqrt{1 - 2 x})}^{- \frac{1}{2}} (\frac{d}{d x} {(1 - 2 x)}^{\frac{1}{2}})) = \frac{1}{2} {(1 + \sqrt{1 + \sqrt{1 - 2 x}})}^{\frac{- 1}{2}} (\frac{1}{2} {(1 + \sqrt{1 - 2 x})}^{- \frac{1}{2}} (\frac{1}{2} {(1 - 2 x)}^{- \frac{1}{2}} (- 2))) = \frac{1}{2} {(1 + \sqrt{1 + \sqrt{1 - 2 x}})}^{\frac{- 1}{2}} (\frac{1}{2} {(1 + \sqrt{1 - 2 x})}^{- \frac{1}{2}} ({(1 - 2 x)}^{- \frac{1}{2}})) = - \frac{1}{4} {(1 + \sqrt{1 + \sqrt{1 - 2 x}})}^{\frac{- 1}{2}} (\frac{{(1 + \sqrt{1 - 2 x})}^{\frac{- 1}{2}}}{\sqrt{1 - 2 x}}) = - \frac{1}{4 \sqrt{1 + \sqrt{1 + \sqrt{1 - 2 x}}} \sqrt{1 + \sqrt{1 - 2 x}} \sqrt{1 - 2 x}}$

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 the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
$f (x) = \sqrt{1 + \sqrt{1 + \sqrt{1 - 2 x}}}$

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

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Statistics

Decision Maths

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

91影视

Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating. f(x)=1+1+1-2x

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

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Statistics

Decision Maths

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

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