how to prove this differential expression

[transgalactic]

[D H]

transgalactic,

 

You should have posted this in the Homework Help section and you should read the rules for homework:

 

A simple reminder to all: this is the "Homework Help" forum, not the "Homework Answers" forum. We will not do your work for you, only point you in the right direction. Posts that do give you the answers may be deleted.

 

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Please show some work.

[transgalactic]

i know that

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

 

 

??

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[Bignose]

The differential to a power means repeated operations of the differentiation operation:

 

[math]\frac{d^n}{dx^n}=\frac{d}{dx}(\frac{d}{dx}(\frac{d}{dx}...))) [/math] where there are n total differentiations performed.

 

for example

 

[math]\frac{d^3 f(x)}{dx^3} =\frac{d}{dx}(\frac{d}{dx}(\frac{df(x)}{dx})) [/math]

 

You should be able to start taking derivatives of the function you have there and a pattern emerge after repeated differentiation.

[transgalactic]

but this pattern is not a way of prooving that this expression is true

??

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