Question

What is the easiest proof of the chain rule?

Answer 1

u could prove it by taking an example?

Answer 2

you have anything to say Joe?

Answer 3

trying to think of a proof right now.

Answer 4

we can use partial derivatives method right? take a small difference and then the difference tends to zero something like that?

Answer 5

i just looked up the proof, its not trivial at all, its pretty complicated.

Answer 6

really we had it in grade 12 it was a simple proof, i dont have the book now i will dig it in the net, it was pretty easy joe

Answer 7

http://www.math.hmc.edu/calculus/tutorials/chainrule/proof.pdf

Answer 8

I guess the proof i have is complicated because its done from a real analysis perspective.

Answer 9

can u link me with that proof?

Answer 10

btw hello joe met u after long lol

Answer 11

@beewaug was that link helpful?

Answer 12

its from a book, let me scan it.

Answer 13

@akshay Somewhat but I don't think that we have gotten far enough with whatever the e symbol is to be completely okay with it. But thatnk you!

Answer 14

it is just a symbol, dont worry about it, it is just a very very small number

Answer 15

well i can think of a proof but i don't think it is consider formal and you might need alittle more stuff

Answer 16

have a look at the link myininaya

Answer 17

i like that akshay

Answer 18

that was our proof we were taught in grade 12

Answer 19

The first two pics are a lemma needed for the proof, and the last pic is the proof. This is from a Real Analysis view. The trick they use is:\[\frac{g(f(x+h))-g(f(x))}{h} = \frac{g(f(x+h)-g(f(x))}{f(x+h)-f(x)}\cdot \frac{f(x+h)-f(x)}{h}\]

Answer 20

yea cool trick!

Answer 21

yes joe thats what i was thinking to do

Answer 22

great job

Answer 23

i dont deserve any credit lol, i got it from a book.

Answer 24

but it is a bit complicated?

Answer 25

am i green to you guys <.< why am i green?

Answer 26

no

Answer 27

no myininaya is green

Answer 28

hi joe!! met u after long!! @myinanaya :D

Answer 29

LOL

Answer 30

r u in any other group?

Answer 31

Linear ALgebra and Feedback.

Answer 32

r u a group mod there?

Answer 33

dont think so o.O

Answer 34

are the top member there is what i mean

Answer 35

how would i be able to check that?

Answer 36

go to that group and see

Answer 37

in the user list