Derivatives of all hyperbolic functions (proofs)

Derivatives of all the hyperbolic functions (derivatives of hyperbolic trig functions), namely derivative of sinh(x), derivative of cosh(x), derivative of tanh(x), derivative of coth(x), derivative of sech(x), and derivative of csch(x).
Remember the hyperbolic cosine and hyperbolic sine are defined to be the x and y values on the unit hyperbola x^2-y^2=1, thus we have the identity cosh^2(x)-sinh^2(x)=1. For more detail, please see this hyperbolic trig function introduction: 👉 • Introduction to Hyperb...
The derivative canvas print: 👉 bit.ly/derivativesonwall
0:00 hyperbolic function identities
1:43 d/dx(sinh(x))
3:09 d/dx(cosh(x))
4:27 d/dx(tanh(x))
6:29 d/dx(coth(x))
8:10 d/dx(sech(x))
9:45 d/dx(csch(x))
11:18 derivatives for you!
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[@DStyle4]

I love this channel! It is a great learning resource for me!

[@bprpcalculusbasics]

Glad to help!

[@byronrobbins8834]

​@@bprpcalculusbasics shine and cosh would simply alternate.

[@subrat0001]

I like his way of changing markers from a single hand.

[@aphelmusonda5253]

thank you for teaching me in just 11 minutes (watching from zambia)

[@aphelmusonda5253]

this man is very intelligent, just the way he is spining the two markers in his hand makes me feel high

[@njengagachanja7197]

Great video👍👍 watching from Kenya

[@rakuziio_art]

See how smooth is he, switching the marker. Love it.

[@tsionaddisuka]

This is amazing video 😮 watching from Ethiopia

[@09neptune]

very clear explanation thank you

[@pouyamohajer9643]

Hi
Im from iran and this video is beautiful
Thanks

[@yacobbezebihe8678]

Thank you!

[@cosmicvoidtree]

Hey love your channels, I’ve learned more calculus from your channels than I have at school (because I haven’t actually gotten to calculus yet). Anyway I had a video idea, since you just did derivatives of inverse trig functions recently, I thought doing the inverse of the error function (just the integral part of the definition for simplicity). I tried this myself similar to how you did the inverse trig function but got stuck when I got to dy/dx=1/e^-y^2. Maybe you could try this and see if you have any luck with it? Thanks for being a great math channel.

[@nitayweksler3051]

Hi. I would like to try it for fun, what is the function?

[@ravisharaghavan8010]

Nice video man

[@unusuallyy]

simply genius 🥰🥰🥰🥰

[@user-wu8yq1rb9t]

Thank you teacher

[@manjulabhata3736]

Thank you sir

[@physcialsciencetutor9750]

The guy is wow in explaination

[@muhamadsadulla]

Thank for you

[@blackstarice]

amazing

[@kibromhabtamu]

hy am josh and i like your pronounsation

[@MrJSSMiller]

Hey my name is Josh!

[@montaha468]

I liked it

[@erroraftererror8329]

I looked up how to pronounce the hyperbolic trig functions one time. Sech is pronounced exactly as it's spelled with the ch as it is normally prounounced in the English language. Csch is pronounced like sech but with the co- prefix in front of it. Coth is pronounced exactly as it is spelled, just like sech. Like "kawth".

[@rogerkearns8094]

Yes, not sech a difficult pronunciation after all. ;)

[@erroraftererror8329]

@@rogerkearns8094 I see what you did there.

[@rogerkearns8094]

@@erroraftererror8329
There's no fooling you. ;)

[@Schnikle_fritz]

What about tanh?

[@erroraftererror8329]

@@Schnikle_fritz Like “tanch”. Rhymes with the condiment ranch.

[@Meander_Man]

4:24 why Is he holding Pokeball if he is using duster

[@YousefIlIl]

It's a microphone.

[@MathAdam]

Is this really ALL of them? Or is this... (wait for it!)... hyperbole? 😜

[@JoshT13]

This is josh

[@fanamatakecick97]

The way i look at hyperbolas, they’re inverse ellipses

[@thomasolson7447]

I'm thinking the hyperbolic functions are just regular old fashioned trig functions with complex numbers. Take a look at e. Two of those are imaginary, and the last one has a sign change because of this.

[@SuperYoonHo]

Yeah! BPRP NORMAL

[@JohnDoe-hd6ly]

Very helpful. But I have to ask the ultimate question. Who’s in the poke ball

[@carultch]

It's his microphone.

[@surajjani4868]

How to solve integration within a minute?

[@allenjonesstyles6112]

Practice brother

[@surajjani4868]

Where are you from bro?

[@chrollokillua3945]

Pokeball :D !!!

[@awenomer9818]

Are you a Muslim ☪️?

[@m3nny125]

Good question i also started to wonder about that a while ago, i suspect he is but i'm unsure. barely any taiwanese are muslims, but at the same time he had a very long beard grown out, and he cut it at around the same time countries like china/surrounding china started being really strict on muslims and regulating what they can and can't do in stuff like growing your beard really long. he also clearly has a decent degree of respect for arabs as seen by him selling his algebra shirt in the original arabic word (الجبر) so he could be muslim but i'm not sure. I really hope he is though as he is a great teacher especially in calculus.

[@tsionaddisuka]

This is amazing video 😮 watching from Ethiopia