Your Teacher LIED! This Derivative IS Easy

In this video, we'll solve this calculus 1 derivative of sin(x) using the first principle! I'll make this differentiation problem easy for you to understand in just a few minutes so you can ace this on your next ap calc exam! We'll use the squeeze limit theorem to assist us in the proof, along with a famous trig identity for sin. Be sure to ninja kick that subscribe button so you don't miss out on more helpful tips for your calc ab exam!

0:00 - Intro
0:10 - First Principle Definition
0:20 - Plugging in h
0:44 - Sin Trig Identity
1:20 - Factoring Expression
1:55 - Splitting The Limit
2:20 - Bring Out X Terms
2:43 - Squeeze Limit Application
3:32 - Cos(h) Limit
4:55 - Sin^2(h) Identity
5:36 - 3 Limits

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[NumberNinjaDave]

BONUS Question: In the step where we had the limit as h approaches 0 of (cos(h)-1)/h, what would the limit have been if there was no -1 term?

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[bobbilly]

You need to explain where you get the sinh/h limit result to avoid circular reasoning because it is usually proven by L'hopital's which uses the derivative of sin.

If you want to use that limit result without L'hopital, the next best thing is using the geometric argument+squeeze theorem method, so you might wanna explain that upfront, otherwise this feels a bit shady since the limit is not "easy".

[cankaankaya]

photo on the cover is not the thing you solved. dy/dx(sinx) != dsinx/dx.