If is a function defined for all and such that

prove that we must have

for some constant .

* Proof. * Let . Then we can compute the derivative,

Since we know we then have

Therefore, for some constant and we have

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Stumbling Robot

A Fraction of a Dot
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Prove that a function satisfying a given equation must be the exponential function

If is a function defined for all and such that

prove that we must have

for some constant .

* Proof. * Let . Then we can compute the derivative,

Since we know we then have

Therefore, for some constant and we have