Math Explanation

[ILC]

Anyone mind explaining to me why it is that e remains constant yet is not a constant in calculus (i.e. it remains the same in derivatives and integrals)? It was explained to me a long time ago, but I can not remember the reason. Thanks.

ILC

[J-Excel]

Could be in how you approach e. Kind of like how 0/0 could be a number of things depending on how you approach 0.

[jkrohn]

e is a constant in the sense that any number is a constant.
First off, e is a number, just like pi is a number.

e ~= 2.71828

Remembering that e is a number, any function of e^x evaluates as any other constant.

d/dx ( 2^x) = ln(2) * 2 ^ x is how you would do a number to an exponent, but since ln(e) = 1 (they are inverses)
d/dx (e^x) = ln(e) * e^x = e^x

Also,
d/dx (2^2x) = 2 * ln(2) * 2^2x
so in turn, d/dx (e^2x) = 2 * ln(e) * e^2x

e evaluates exactly the same as anything else, its just that ln(e) = 1 allowing for simplification.

The same applies for integrals if you would like to step backwards

Jkrohn

[ILC]

Alright, now I see the reasoning. Thanks.

ILC