If we are finding the derivative of a function f(x) analytically at a certain point x , we would differentiate to find , and then evaluate our new expression at our desired value of . However, there are some functions that are nearly impossible to analytically, so numerical differentiation will be necessary. There are three different methods we will cover: Backward Difference Methods Forward Difference Methods Central Difference Methods We will also discuss finding numerical derivatives with higher order approximations as well as higher order derivatives