# How to prove this differential expression

1. Jan 24, 2009

### transgalactic

i need to prove that this expression is correct

http://img216.imageshack.us/my.php?image=23051510gd6.gif

f'(x)=d(f(x))/dx
there is no such structure on the left side of the equation
there are a defferential in the power of n
only the d^n

??

2. Jan 24, 2009

### Mute

The first thing I would try is the Liebniz product rule:

$$\frac{d^n}{dx^n}(fg) = \sum_{k=0}^n \frac{n!}{k!(n-k)!}f^{(k)}g^{(n-k)}$$

where $f^{(j)}$ is the jth derivative of f. See if that gets you anywhere.

3. Jan 24, 2009

### Staff: Mentor

... or maybe a proof by induction.

4. Jan 24, 2009

### transgalactic

Last edited by a moderator: May 3, 2017
5. Jan 25, 2009

### transgalactic

Last edited by a moderator: May 3, 2017