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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

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