The PROOF that the Derivative of sin(x) is cos(x)!!! | Limit Definition of Derivatives

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Let's prove that the derivative of sin(x) is cos(x)!!!

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Check also this video!!! 🤩🥳🎉🎊🎈⬇️

Let me know if you want to see the proof of lim x->0 ((sinx)/x)) and lim x->0 ((cosx - x)/x)😉🎉🎊🎈

JonnyMath
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Never seen a minecraft character explain a derivative, but alright i guess 😂

giacomomosele
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.y=sinx, berarti y+dy=sin(x+dx)=
=sinx cos dx+cosx sin dx.
Untuk dy-->0 berarti dx-->0 dan
.cos dx--->cos0°=1 : serta sin dx-->dx
Sehingga untuk dx-->0
.y+dy=y.1+cosx.dx
.dy=cosx dx
.dy/dx=cosx atau
d(sinx)/dx=cosx

NurHadi-qfkl
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Instead of using sin(x+h) expression, you could use sin(x+h) - sinx = 2cos(x+h/2) × sin(h/2)

hydroq
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But. Then again, we cannot fundamentally say thet
(cos h - 1 )/h is 0. Because we either need series expansion which could have easily proven the derivative or use L' rule which says that derv of cos h is -sin h (which again is a question in itself )...

mathslover
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we could also use the fundamental trigonometry theorem to solve the (cos - 1) part i tried myself and it worked :)

Fofodoido
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You pulled two less famous facts out of the air to prove a far more common fact. You can use geometry to prove those two, much more satisfying.

idjles