How to prove this differential expression

[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??

 

[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.

 

[Mark44]

... or maybe a proof by induction.

 

[transgalactic]

http://img300.imageshack.us/img300/7462/18573825tp3.th.gif

 

[transgalactic]

http://img183.imageshack.us/img183/4918/84224186ed5.th.gif