page 1 of 3
One truly remarkable characteristic of e ^{x} is that
e ^{x} = e ^{x} |
Besides the trivial case of f (x) = 0 , e ^{x} and its constant multiples are the only functions whose derivatives are equal to themselves!
Incorporating the principles of the chain rule, we might also say that if u is a function of x , then
e ^{u} = e ^{u} |
By extension, e ^{x} dx = e ^{x} + c . Using the fact that
e ^{u} = e ^{u} |
we can derive a more general formula for the derivative of a ^{x} , where a is any positive constant.
First, note that a ^{x} can be rewritten as
Take a Study Break!