How do you intuitively draw the derivative?

[DiyTech]

I was wondering how would you step by step intuitively draw the derivative?

 

[Dr.Peterson]

Please give an example of the kind of problem you are asking about; and it will be helpful if you can show us your attempt at it, so we can provide the specific help you need, and not tell you things you already know.

 

[HallsofIvy]

If you mean "given a graph of f(x) rather than a formula, how would you draw a graph of f'(x)?" then you would use the fact that the deriative of a function depends on how sharply the function graph goes up or down. That is, where the graph of the function is increasing the derivative is positive, the faster the graph is increasing, the more positive the derivative is. Where the graph of the function is going down, the derivative is negative, the faster the graph is decreasing, the more negative the derivative is. Where the function is level, the derivative is 0.