Partial derivatives

Until now we've been working with univariate functions, but the type of function we will mostly work with from now on will be multivariate, as the dataset will contain much more than one column and each one of them will represent a different variable.

In many cases, we will need to know how the function changes in a relationship with only one dimension, which will involve looking at how one column of the dataset contributes to the total number of function changes.

The calculation of partial derivatives consists of applying the already known derivation rules to the multivariate function, considering the variables are not being derived as constant.

Take a look at the following power rule:

f(x,y) = 2x3y

When differentiating this function with respect to x, considering y a constant, we can rewrite it as 3 . 2 y x2, and applying the derivative to the variable x allows us to obtain the following derivative:

d/dx (f(x,y)) = 6y*x2

Using these techniques, we can proceed with the more complex multivariate functions, which will be part of our feature set, normally consisting of much more than two variables.