# Why is this true?

pivoxa15

## 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?

Homework Helper
You may want to investigate the chain rule.

pivoxa15
Could you possibly be a little bit more specific?

Homework Helper

## 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!

You may want to investigate the chain rule.

Could you possibly be a little bit more specific?
Are you saying you have never heard of the chain rule? You are being asked to prove the chain rule!
$$\frac{dc}{dx}= \lim_{h\rightarrow 0} \frac{c(x+h)- c(x)}{h}$$
"Before" the limit, this is a fraction- you can cancel before the limit but be careful, this is not a trivial proof.

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pivoxa15
I have heard of the chain rule.

In fact I realise that the chain rule is just what I stated (d/dx)c=(d/da)c(da/dx)

pivoxa15
"da/dx" and "dc/da" are NOT fractions so it is not corret to say that the "da" cancels!

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"?