A Fun Little Party Trick

Calculus Level 1

\[\dfrac{d}{dx} (A^{x}) = A^{x}\]

Suppose that for a particular value of the constant \(A\) the equation above is true for all \(x\). Determine the value of \(A\) to three decimal places.

Note: You probably know right away what the answer is. But try to derive it using difference quotients, as suggested above, and then post your solution. Good for impressing friends who haven't seen it before.

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