If you are given a graph of a function, how do you draw the derivative?

Answer 1

You measure the slope of the graph, then graph the slope.

http://people.hofstra.edu/stefan_waner/Realworld/calctopic1/derivgraph.html

Answer 2

Break the graph up into a bunch of increments, each with the same x-axis distance between them. The more the graph flips from up to down, the more increments you need. (The more you have, the better your derivative graph will be.) Write down the (x,y) coordinates of each point. Find the slope between each set of points by taking the rise/run: (y2-y1)/(x2-x1). Plot these points directly between each division you made before. As an example, suppose you initially broke the graph up at each whole number (x=1, x=2, x=3 etc) then your derivative points need to go at x=1.5, x=2.5, x=3.5 etc. Connect these points with a smooth line, and you're done.