Derivative Proof of ax

This proof is similar to ex. In fact, e can be plugged in for a, and we would get the same answer because ln(e) = 1.

Derivative proof of ax

Rewrite ax as an exponent of eln

Use Chain Rule and substitute u for xlna

Cancel out dx over dx, and substitute back in for u

Bring down the ax

Here is a graph of f(x) = .5x and f(x) = 2x and their derivatives.

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