To estimate the derivative of a function, you can use the definition of the derivative: the limit as h goes to 0 of (f(a+h)-f(a))/h.
First, evaluate the function at a. Then, you can calculate (f(a+h)-f(a))/h for various values of h, as h gets smaller and smaller. As h gets smaller, it approaches 0 without ever actually being equal to 0. This expression will get closer and closer to some number, which we say is an estimate of the derivative of a function.