Q. 22 Find the derivatives of each of ... [FREE SOLUTION]

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Chapter 2: Q. 22 (page 233)

Find the derivatives of each of the functions in Exercises 17鈥�50. In some cases it may be convenient to do some preliminary algebra.
$f (x) = \sec^{2} (x^{- 1}) .$

Short Answer

Expert verified

$T h e v a l u e o f t h e d e r i v a t i v e i s : - \frac{2}{x^{2}} s e c^{2} (\frac{1}{x}) \tan (\frac{1}{x}) .$

Step by step solution

Step 1. Given Information.

$f (x) = \sec^{2} (x^{- 1}) .$

Step 2. General formulas for finding derivatives.

$\frac{d}{d x} (x^{n}) = n x^{n - 1}, \frac{d}{d x} (\sin x) = \cos x, \frac{d}{d x} (\cos x) = - \sin x, \frac{d}{d x} (\tan x) = s e c^{2} x, \frac{d}{d x} (s e c x) = s e c x \tan x, \frac{d}{d x} (c s c x) = - c s c x c o t x, \frac{d}{d x} (c o t x) = - c s c^{2} x, P r o d u c t r u l e : \frac{d}{d x} (u v) = u \frac{d v}{d x} + v \frac{d u}{d x}, Q u o t i e n t r u l e : \frac{d}{d x} (\frac{u}{v}) = \frac{v \frac{d u}{d x} - u \frac{d v}{d x}}{v^{2}}, C h a i n r u l e : \frac{d}{d x} (f o g (x)) = \frac{d}{d x} (f (g (x))) 脳 \frac{d}{d x} (g (x) .$

Step 3. Solving derivative using above formulas.

$f (x) = s e c^{2} (x^{- 1}) = s e c^{2} (\frac{1}{x}) D i f f e r e n t i a t i n g u \sin g c h a i n r u l e w e g e t, \frac{d}{d x} (f (x)) = 2 s e c (\frac{1}{x}) \frac{d}{d x} (s e c (\frac{1}{x})) = 2 s e c (\frac{1}{x}) s e c (\frac{1}{x}) \tan (\frac{1}{x}) \frac{d}{d x} (\frac{1}{x}) = 2 s e c (\frac{1}{x}) s e c (\frac{1}{x}) \tan (\frac{1}{x}) (\frac{- 1}{x^{2}}) = - (\frac{2}{x^{2}}) s e c^{2} (\frac{1}{x}) \tan (\frac{1}{x}) .$

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91影视

Find the derivatives of each of the functions in Exercises 17鈥�50. In some cases it may be convenient to do some preliminary algebra.
$f (x) = \sec^{2} (x^{- 1}) .$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. General formulas for finding derivatives.

Step 3. Solving derivative using above formulas.

One App. One Place for Learning.

Most popular questions from this chapter

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91影视

Find the derivatives of each of the functions in Exercises 17鈥�50. In some cases it may be convenient to do some preliminary algebra.f(x)=sec2x-1.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. General formulas for finding derivatives.

Step 3. Solving derivative using above formulas.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Logic and Functions

Geometry

Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Find the derivatives of each of the functions in Exercises 17鈥�50. In some cases it may be convenient to do some preliminary algebra.
$f (x) = \sec^{2} (x^{- 1}) .$