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

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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

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

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what text are you using?
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
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very nice. not a proof though
what if h is a constant function? that is the problem with all these proofs
wait whats very nice but not a proof
brittT myinanaya has it, use that one
use what myinanaya wrote. it is good
that is very helpful!
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
oh by the way that is suppose to say deltax->0 not h->0 o nthat attachment
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
oh yeah f(g(0)) i don't think will work i understand
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
see serge lang calculus if you want a real proof. that is why i asked what text you were using. use myinanaya's proof.
or i mean it doesnt have to be zero but a constant yeah
http://www.mathnotes.org/index.php?pid=64#?pid=64
the first one is my proof yeah! lol
part of
i will be willing to bet cash that it is the proof in the text brittT is using
better explanation of what is wrong http://math.rice.edu/~cjd/chainrule.pdf
the flaw is that if \[g(x)=c\] a constant, then the denominator is identically 0
i am using what myininaya posted

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