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acmilan

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We all know d/dx x2 = 2x

But what if we define x2 = x + x + ... + x (x times)

Then d/dx x2 = 1 + 1 + ... + 1 (x times) = x

:O

Can anyone explain? ;)
 

acullen

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acmilan said:
We all know d/dx x2 = 2x

But what if we define x2 = x + x + ... + x (x times)

Then d/dx x2 = 1 + 1 + ... + 1 (x times) = x

:O

Can anyone explain? ;)
This one is screwing with my head. My guess is that you cannot treat a variable as though it were a constant.

Written differently, it should yield the same result:

i.e. sin(x) = x - x3/3! + x5/5!-...+...etc...

this differentiated will give:
d/dx sin(x) = 1 - x2/2! + x4/4! - ... + ... etc...
which is equal to cos(x) = d/dxsin(x)
 

webby234

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I think you need to use the product rule as you are not adding x a constant number of times, but a variable amount of times. You must take into acount that as x changes, so does the number of additions. In other words you have x times x.

u = x u' = 1
v = x v' = 1

d/dx = x + x = 2x

Clever though.
 

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