Behavior of f(x) = bx

Let f(x) = bx. Then the derivative of f has the property that f '(x) = f '(0) bx.

Below is the plot of f(x) = bx, its derivative f '(x) = (m) bx, as well as a tangent line at x = 0. The tangent line has slope m = m, as f '(0) = m. Move the slider to change the base. What value of b yields f '(0) = 1?

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