basic calcus?

0 ⤊

if i have a graph that is one to one, lets say y=f(x) and another graph z=g(x), many to one. can i say that the derivative of dz/dy = (dz/dx)*(dx/dy).

2007-03-04 03:39:28 · 3 answers · asked by Anon 1 in Science & Mathematics ➔ Mathematics

3 answers

z = g(x) = g[f^-1(y)], because y = f(x) is one to one.

Therefore,
dz/dy = (dz/dx)(dx/dy), derivative of composition function.

2007-03-04 03:56:41 · answer #1 · answered by sahsjing 7 · 0⤊ 0⤋

That works.

2007-03-04 11:46:14 · answer #2 · answered by Rando 4 · 0⤊ 0⤋

yes, it is called the chain rule

2007-03-04 11:56:19 · answer #3 · answered by SS4 7 · 0⤊ 0⤋