Very good presentation! I am a long practitioner of math, including the calculus, and use the chain rule quite instinctively. However the why evaded me me until recently. Your video helps. Two salient points helped me. (a) The chain rule is directly connected to composition functions b) The definition of a derivative function, is directly linked to a limit. Also I appreciate more the importance of differentiability and continuity. Thank you!
@punditgi2 жыл бұрын
Unfortunately the second denominator csn be zero if an interval exists around x whrre f is constant.
@zhangkevin6748 Жыл бұрын
Case work the rest
@andreferreira83257 ай бұрын
But since we are dealing with that situation using limits solves that a problem,right?
@Avighna7 ай бұрын
this would imply that g'(x) is 0, right? and this would also imply that (f(g(x))' is 0, so the formula (f(g(x))' = f'(g(x)) g'(x) trivially holds true (0 = f'(g(x) * 0 ==> 0 = 0)
@bassmaiasa13128 ай бұрын
The first step of the proof is not jumping out at me. In the definition of f', I would start with "g(x+h) - g(x)" as the denominator. How does h = g(x+h) - g(x)?
@Samir-zb3xk8 ай бұрын
As far as im aware there isnt a derivative definition where you start with g(x+h)-g(x) in the denominator. The one he used is pretty standard
@JasurZero7 ай бұрын
If I understood correctly, h isn't equal g(x+h)-g(x). But if h→0 => g(x+h)-g(x)→0. So we could change h→0 to g(x+h)-g(x)→0.
@micahchaya3909 Жыл бұрын
Sweet! Thanks for explaining that. Love proofs. Makes it easier to appreciate all the rules
@haasjeoverkonijn69616 ай бұрын
Nice. But what is the font you use? I d like to use it in a report as well. Thanks!