Derivative of exponential function
This interactive plot illustrates the fact that the derivative of the exponential function (e^x) is also the exponential function. In other words, the gradient of the tangent at any point is equal to the value of the function at that point.
The plot below illustrates this. View the script here
The blue curve is the exponential function. The red line is the tangent to the curve. The gradient of this tangent can be calculated from the lengths of the 2 lines A and B
gradient = A / B
Click and drag the green control point to move the tangent. Notice that the length of A changes, but the length of B is always exactly 1. The gradient is that case is given by the length of A, which of course is equal to e^x.