Derivative of Exponential Functions
This applet is designed to study the relationship between the graph of exponential functions and their derivatives.
The function graphed in red is the graph of the exponential function \(f(x) = a^x\), where the base value \(a\) can be changed using the slider below the graph. Also shown (in blue) is the tangent line to the graph at \(x = 0\) and, below the slider, the value of the slope \(m\) of the tangent line. This slope is the derivative of the function at \(x = 0\), \(f'(0)\). By moving the slider, we can see how the base affects the graph of the function and its derivative at \(x = 0\).