Differentiation
In the following section, we will look at how to solve differentiation and some of its applications.
Getting ready
There are three ways to approach the computation of derivatives:
Numerical differentiation refers to the process of approximation of the derivative of a given function at a point. In SciPy, we have the following procedures, which will be covered in detail:
For generic univariate functions, there is the central difference formula with fixed spacing.
It is always possible to perform numerical differentiation via Cauchy's theorem, which transforms the derivative into a definite integral. This integral is then treated with the techniques of numerical integration explained before.
Symbolic differentiation refers to computation of functional expressions of derivatives of functions, pretty much in the same way as we would do manually. It is termed symbolic because unlike its numerical counterpart, symbols take the roles of variables rather than numbers or vectors of numbers...
