Derivative of cosh^-1(x), two ways

Показать описание

We will find the derivative of inverse hyperbolic cosine in two ways.

10% off with the code "WELCOME10"

Рекомендации по теме

Комментарии

I want that shirt. Wait, no, I want the person in front of me to have that shirt.

kingbeauregard

Derivative of arccosh x is -arcsinh x *dabs*

futfan

this video just saved me from depression

lekonokago

are students allowed to wear that shirt during tests? xD

BigDBrian

I liked the second one... don't know, I have always liked more implicit (don't know how to write it) derivatives... Great video!

YourPhysicsSimulator

Can you do a video of this showing the general equation for the derivative cosh^-1x?

nvapisces

Does anyone have the link for buying that t-shirt

PhilipLabelle

Do You Wear this shirt when you are invigilator in any exam?

purushotamgarg

Hello sir from india how we will solve underroot r4-a4 please answer

tanuyadav

I had an idea for a video on a "concatenate" operator, a function that just puts 2 things together. For example, concat(2, 2) = 22, concat(47, 299) = 47299, etc.
I'm not sure how to derive a function for this, and it may be interesting.

JoJoJet

how are you able to rewrite cosh^-1 to ln(x+sqrt(x^2-1)? I didn't now that is a thing

PlainVas

The third way is to use that cosh(x) = cos(ix), thus cosh^-1(x) = -i cos^-1(x). Now,

d/dx cosh^-1(x) = d/dx (-i cos^-1(x))
= -i d/dx cos^-1(x)

But by trigonometry (draw a triangle diagram and use trig identities), d/dx cos^-1(x) = -1/sqrt(1 - x^2). Then d/dx cosh^-1(x) = i/sqrt(1 - x^2), and noting that when |x| >= 1 we have sqrt(1 - x^2) = i sqrt(x^2 - 1), we get d/dx cosh^-1(x) = 1/sqrt(x^2 - 1), |x| >= 1. Done. Complex Analysis FTW.

mikety

Now when you say "chain rule" it sounds wrong

Gold

I haven't testet it out, but I have a problem for you:
(f^-1(x))' = (f(x)') ^-1

Leon-nnjq

Show that cosh^- 1 (1/x) = sec(h ^ - 1) * x

udynkhanikar

The second method is way cooler, because i don't need to remember anything

perveilov

find the definite integral of this derivative and youll have a little surprise :D

karinanostan

I got 1/sinh(arccosh(x)) amirite

Edit: No
Edit again: Yes

xxfazenoscoperdoesnosco

Derivative of cosh^-1(x), two ways

Derivative of cosh^-1(x), two ways

Derivatives of Inverse Hyperbolic Functions

Q14, derivative of sinh^-1(x), two ways

Derivative of Inverse Hyperbolic Trigonometry: cosh^-1(x)

Derivatives of Hyperbolic Functions

Derivative of cosh^(-1)(5x) #shorts

Derivative of cosh (x^2+1) || Differentiation of Hyperbolic Trigonometric Functions

Inverse hyperbolic cosine [cosh^-1(x)] as a logarithm

Evaluating Inverse Hyperbolic Functions

Find derivative of y= cosh^(-1) sqrt(x). Inverse Hyperbolic Functions

derivative of inverse hyperbolic sine | bprp calculus

Find derivative for y = x coth(1+ x^2). Hyperbolic functions

Inverse cosh(x)

Sect 3 11 #39, derivative of (1-cosh(x))/(1+cosh(x))

Find derivative of y = cosh^(-1) (2sqrt(x+1)) with respect to x. Inverse Hyperbolic Functions

Derivative of cosh(x)

Trigonometric limit - lim(cosh-1)/h

Find derivative of y= cosh^(-1) (sec x) with respect to x. Inverse Hyperbolic Functions

Differentiation of inverse cosh (cosh^-1(x))

Derivative of sinh(cosh(x)) #shorts

When mathematicians get bored (ep1)

The Derivative of the Inverse Hyperbolic Sine

Derivative of inverse hyperbolic tan(x) | Differentiation

HOW DO YOU DIFFERENTIATE arcosh(x)? (INVERSE HYPERBOLIC COSINE, HYPERBOLIC FUNCTIONS, COSH, ARCOSH)