At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
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!
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
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
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
the first one is my proof yeah! lol
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