Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Use the following information. The hyperbolic sine of $u$ is defined as $\sinh u=\frac{1}{2}\left(e^{u}-e^{-u}\right)$ Figure 27.30 shows the graph of $y=\sinh x$. The hyperbolic cosine of $u$ is defined as $\cosh u=\frac{1}{2}\left(e^{u}+e^{-u}\right)$ Figure 27.31 shows the graph of $y=\cosh x$. These functions are called hyperbolic functions since, if $x=\cosh u$ and $y=\sinh u, x$ and $y$ satisfy the equation of the hyperbola $x^{2}-y^{2}=1$. Show that $\frac{d}{d x} \sinh u=\cosh u \frac{d u}{d x}$ and $\frac{d}{d x} \cosh u=\sinh u \frac{d u}{d x}$where $u$ is a function of $x$.

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 6

Derivative of the Exponential Function

Derivatives

Missouri State University

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

05:33

Hyperbolic Cosine Function…

02:05

The hyperbolic cosine func…

02:40

02:39

In calculus, we study hype…

02:11

03:51

The hyperbolic sine functi…

03:39

The hyperbolic in hyperbol…

03:20

06:12

The hyperbolic cosine and …

19:30

Hyperbolic Functions The h…

for this question That's also still with the graph of the function y equals two into the bull X and no, first to get the graph off the function Y t ah, exchange a car. Why Tuesday won't over to see to the parole fax And before this new function, we need to shrink. The graph of whyy goes to e x vertically by a fact off 1/2, which means each points off the new function this green function. Why value become half off the previous one off this brat function. So for the special point like here, the previous function must go across the points 01 one. Now the new function just drink. Whoa ha! Wish means the new function must go across a point they will want over, huh? So let's get a new graph here. Yet the green line is a graph off. The one equals to walk over to eat it, throw off acts so similarly we can get why equals to one over to e to the post minus X uh, eat his home minus x just ah, in another direction here. So the blue lioce grapple. Wyche was toe t to the Po from minus X. And now we can use the graphic audition together our new function. Why you close to won't Todt Home acts Claus. Well, t to 12 minus x. It actually s our up to function, Coach X. So you see, use a spool lying Teoh This red line, which means each off the point should add a little bit like this. A little bit A little bit a little Billy Billy. It will beat something like that. You will see Here's ings issue off the green line, boo Like go across So point Ah, the robot over two. So this real I should go over Well, two plus one or two it was one this one point. So just like this? No. And there's to function together. You get ah, I gather graph off the object function the coche excess function. So they say so question a The question be is used the definition to shoot kohsh Um minus X equal suu coach acts and the way expand by its definition iss Ah e x waas e minus x divided by two Oh, well, sorry. Let's go back. Use a definition to expand the coach function we get to here's e to pull off minus two Kloss e to the polls minus the minus X. Then you can get this minus minus ISS plus and the chance the water you were gods e x plus e to the post minus X and they actually the cold X.

View More Answers From This Book

Find Another Textbook

In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

Hyperbolic Cosine Function The hyperbolic cosine function is defined by$…

The hyperbolic cosine function is defined by $$\cosh (x)=\frac{e^{x}+e^{-x}}…

The hyperbolic cosine function is defined by $$\cosh (x)=\frac{e^{x}…

In calculus, we study hyperbolic functions. The hyperbolic sine is defined b…

The hyperbolic sine function, denoted by sinh, is defined by the equation $$…

The hyperbolic in hyperbolic functions Just as $x=\cos u$ and$y=\sin u$ …

The hyperbolic cosine function, denoted by cosh, is defined by the equation …

The hyperbolic cosine and hyperbolic sine functions are-defined by$$…

Hyperbolic Functions The hyperbolic trigonometric functions are defined as f…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.