Showing dF/dx = (1/a)dF/du under substitution x = au

[Dyatlov]

Hello.
We have the derivative of a function: d F(x)/dx. If we substitute x = au, how can I show that d F(x)/dx = (1/a) (dF/du) ?

 

[QuantumQuest]

Hello.
We have the derivative of a function: d F(x)/dx. If we substitute x = au, how can I show that d F(x)/dx = (1/a) (dF/du) ?

When you do a substitution, you take the derivatives of both sides (hint: take into account what is constant and what is not). If you do this, you'll immediately come to what you need to show.

 

[Dyatlov]

Thanks for the answer, did it and got:
(dF/da) (dF/du) = (dF/da) u + (dF/du) a = (dF/du) a, since a is a constant. What am I missing here?

 

[QuantumQuest]

Thanks for the answer, did it and got:
(dF/da) (dF/du) = (dF/da) u + (dF/du) a = (dF/du) a, since a is a constant. What am I missing here?

As I previously said, note that $dx = a\cdot du$.

 

[Dyatlov]

Thanks, got it now.