The gradient of a function
Move blue point A to see how the gradient (slope) of the blue function f(x) changes with x. The red point shows the value of the slope. Right click on the red point to turn the "trace on" and sketch out df/dx. Click on the "reset" button (top right corner) and then type in your own functions into the Input: box at the bottom to see how this looks for any function. e.g. Try typing "f(x)=3x^2-2x+1" or "f(x) = exp(x)" or "f(x)=log(x)".
The derivative (df/dx) is given algebraically in the left hand window as f'(x). You can plot it by right clicking on it and choosing "show object".