/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 63 Which hyperbolic derivative form... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 63

Which hyperbolic derivative formulas differ from their trigonometric counterparts by a minus sign?

Short Answer

Expert verified
The derivative formulas of the hyperbolic functions \(\cosh(x)\) and \(\csch(x)\) deviate from their trigonometric counterparts cos(x) and csc(x) by a minus sign.

Step by step solution

01

Identify Hyperbolic Derivative Formulas

List out the derivative formulas for the hyperbolic functions: 1. \( \frac{d}{dx} \sinh(x) = \cosh(x) \)2. \( \frac{d}{dx} \cosh(x) = \sinh(x) \)3. \( \frac{d}{dx} \tanh(x) = \sech^2(x) \)4. \( \frac{d}{dx} \coth(x) = - \csch^2(x) \)5. \( \frac{d}{dx} \sech(x) = - \sech(x) \tanh(x) \)6. \( \frac{d}{dx} \csch(x) = - \csch(x) \coth(x) \)
02

Identify Trigonometric Derivative Formulas

List out the derivative formulas for the trigonometric functions:1. \( \frac{d}{dx} \sin(x) = \cos(x) \)2. \( \frac{d}{dx} \cos(x) = - \sin(x) \)3. \( \frac{d}{dx} \tan(x) = \sec^2(x) \)4. \( \frac{d}{dx} \cot(x) = - \csc^2(x) \)5. \( \frac{d}{dx} \sec(x) = \sec(x) \tan(x) \)6. \( \frac{d}{dx} \csc(x) = - \csc(x) \cot(x) \)
03

Compare and Contrast

Compare the derivative formulas of the hyperbolic functions with their corresponding trigonometric counterpart. One noticeable difference is the presence of a minus sign in the derivative formulas of \(\cosh(x)\) and \(\csch(x) \cosh(x)\) functions as compared to the respective trigonometric derivative formulas of cos(x) and csc(x). Therefore, these formulas stand out as they deviate from their trigonometric counterparts by a minus sign.

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

Most popular questions from this chapter

Find any relative extrema of the function. \(f(x)=\arcsin x-2 x\)

Using a Right Triangle Show that \(\arctan (\sinh x)=\arcsin (\tanh x)\)

Horizontal Motion The position function of a particle moving along the \(x\) -axis is \(x(t)=A e^{k t}+B e^{-k t},\) where \(A, B,\) and \(k\) are positive constants. (a) During what times \(t\) is the particle closest to the origin? (b) Show that the acceleration of the particle is proportional to the position of the particle. What is the constant of proportionality?

Find an equation of the tangent line to the graph of the function at the given point. \(y=\frac{1}{2} \arccos x, \quad\left(-\frac{\sqrt{2}}{2}, \frac{3 \pi}{8}\right)\)

Find the derivative of the function. \(h(t)=\sin (\arccos t)\)
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.