How to draw the derivative for a function?

[MIA6]

If you see a graph of a function, then you need to draw the derivative for this function. How can you draw it? I know you have to find some points, and find their slopes, and then put it on the graph and connect the points, but how can I estimate the slopes. I can only figure out the slope of 0 and positive slope or negative slope. Other than that, I can't tell the slope. Hope you can tell me.
Thanks for help.

 

[EnumaElish]

The derivative at point (x,y) is the slope of the line tangent to the function at (x,y). I think you are concentrating too much on the function itself. Instead try visualizing a straight line that "barely" touches the function at point (x,y). Then calculate the slope of that tangent line.

 

[ice109]

$$\frac{\Delta F(P)}{\Delta P}=\frac{F(P+\Delta P)-F(P)}{\Delta P}$$

there the slope of the line that connects point (F,P) and (F(P+ΔP),P+ΔP). now what happens when ΔP approaches zero?