Help :~( (1 Viewer)

[acmilan]

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]

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]

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.

 

[acmilan]

Good work !