You see here the function f(x) = x^2 and its tangent line a together with slope triangle. Drag Point A with the mouse. This produces a trace of the slope creating the graph of the slope function. Which kind of function is this slope function? Try to find the slope function's equation, too.
Type f'(x) into the input field and press Enter. Choose the "move mode" and drag point A with your mouse again. What is happening? Write down your observations.