Question

i need to prove the chain rule for [f(g(h(x)))]=f'(g(h(x))g'(h(x))h'(x) using the limit definition of the derivative

Answer 1

Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

Answer 2

i don't believe you. this is amazingly hard.

Answer 3

in fact if you look in your text i am willing to bet they do not even prove the chain rule. at some point they will say "it is reasonable to believe that ..." and not actually prove it

Answer 4

what text are you using?

Answer 5

no its proven in my text but i do not understand how to add the third funtion into the given proof and im using calculus early transcendentals by jon rogawski

Answer 6

very nice. not a proof though

Answer 7

what if h is a constant function? that is the problem with all these proofs

Answer 8

wait whats very nice but not a proof

Answer 9

brittT myinanaya has it, use that one

Answer 10

use what myinanaya wrote. it is good

Answer 11

that is very helpful!

Answer 12

satellitle like so you mean if h(x)=5
then no matter what change x happens h will always be the same
so we have lim deltax->0 (5-5)/h=0/h=0

Answer 13

oh by the way that is suppose to say deltax->0 not h->0 o nthat attachment

Answer 14

well my problem also states that they are all differntiable and if it was a constant then it would not work

and yeah i figured thats what you ment thank you

Answer 15

oh yeah f(g(0)) i don't think will work i understand

Answer 16

the problem with all these proof is they ignore what can happen if the "inside function" is a constant. but ignore me because you (brittT) clearly don't have to worry about it. forget i mentioned it. but a rigorous proof of the chain rule is a pain

Answer 17

see serge lang calculus if you want a real proof. that is why i asked what text you were using. use myinanaya's proof.

Answer 18

or i mean it doesnt have to be zero but a constant yeah

Answer 19

http://www.mathnotes.org/index.php?pid=64#?pid=64

Answer 20

the first one is my proof yeah! lol

Answer 21

part of

Answer 22

i will be willing to bet cash that it is the proof in the text brittT is using

Answer 23

better explanation of what is wrong
http://math.rice.edu/~cjd/chainrule.pdf

Answer 24

the flaw is that if \[g(x)=c\] a constant, then the denominator is identically 0

Answer 25

i am using what myininaya posted