Hyperbolic Functions - Derivatives

Derivatives of hyperbolic functions leading up to the problem of the catenary.

Check out www.gaussianmath.com for an indepth study and for more calculus related topics.

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• hyperbolic
• catenary
• donny
• gaussian
• math

[subu12345]

isnt it jus

sinx

cosx

tanx?

[donylee]

These are 'hyperbolic' functions and not the standard trigonometry functions.

We write them as 'sinh x' with a 'h' after 'sin'. They rarely bear connections with the standard trig functions. Their derivations too are hyperbolic functions. The functions themselves are defined in terms of natural log number e and are useful in certain integrations.

See my video 'The Catenary' and you'll know what I mean.

[BlueScience1]

nice work! i wish if you talked in french :)

[donylee]

Hey BlueScience,

I guess you from France. They learn hyperbolic functions there? Hehe.

Thanks for watching.

[Mr62Sam]

lol he says chink instead of sinch

[intellectual1234]

The nickname of hyperbolic tangeant is darn I believe.

sinh=shin

cosh=korsh

tanh=darn

coth=korf

sech=seech

csch=ko-seech

[TeHUnreaL]

Yes, the derivative of coshx is sinhx, not -sinhx. If you take the derivative of the definition of cosh, which is (e^x + e^-x)/2, you get (e^x - e^-x)/2. Which is the definition of positive sinh.

And the tanhx is pronounced the "tanth" of x.

[subu12345]

yeh... isnt when u differentiate

sinx = cosx

cosx =-sinx

tanx = sec^2x

or issit different for sinhx and coshx?

[suzanabdalraheem]

usefull lucter...thank you indeed

[suzanabdalraheem]

r u sure that d/dxcosh=sinh? not -sinh?

[brilliantfranz]

sinx

cosx

tanx are functions made from a basic circunference... (also but rarely called circular functions)

sinhx

coshx

tanhx are functions made from a hyperbole ... (also known as hiperbolic functions)

[killercan7]

Thank you so much man. This is very helpful.

[donylee]

Yup, could be different from different countries. Anyways, I got the pronunciation from George F. Simmons amazing calculus book 'Calculus with Analytic Geometry' where he mentioned that hyperbolic sine is pronounced as 'cinch' which rhymes with 'pinch'.

It looks to have that 'ch' sound from the 'c' in sinc.

[chennol]

lol, its pronouced shine in britain I believe, hes from Sginapore, great lecture though