What's My Favorite Transcendental Number?

Calculus Level 1

For a positive constant \(b\), I draw a graph of \(y = b^x\), on the first quadrant.

I noticed that the gradient of this curve at any point is equal to the value of the function itself. In other words,

\[ \dfrac{d}{dx} y = y .\]

How many possible values of \(b\) satisfy this scenario?

Image Credit: Wikimedia Dmcq.

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