- #1
- 2,255
- 1
Homework Statement
(d/dx)c=(d/da)c(da/dx)
where c=f(a(x))
The Attempt at a Solution
It seems correct because the da cancels but how do you get this from first principles?
"da/dx" and "dc/da" are NOT fractions so it is not correct to say that the "da" cancels!Homework Statement
(d/dx)c=(d/da)c(da/dx)
where c=f(a(x))
The Attempt at a Solution
It seems correct because the da cancels but how do you get this from first principles?
You may want to investigate the chain rule.
Are you saying you have never heard of the chain rule? You are being asked to prove the chain rule!Could you possibly be a little bit more specific?
But physicists and applied mathematicians like to treat them as fractions in the limit. Is it okay to treat them as fractions and specify "in the limit"?"da/dx" and "dc/da" are NOT fractions so it is not corret to say that the "da" cancels!
Yes, because the derivative is the limit of a fraction, you can always treat them "like" a fraction- that's one of the advantages of the dy/dt notation over f '. And, in fact, it is motivation for defining the "differentials", dx and dy= f '(x) dx.But physicists and applied mathematicians like to treat them as fractions in the limit. Is it okay to treat them as fractions and specify "in the limit"?