Course Content

Mathematics for Data Analysis and Modeling

## Mathematics for Data Analysis and Modeling

# Partial Derivative of the Function

## Partial derivative

If we are talking about the functions with multiple arguments, we must consider the concept of **partial derivative**. A partial derivative measures how a function changes with respect to one of its variables while keeping the other variables constant. It is a concept used in multivariable calculus to analyze the rate of change of a function in multiple dimensions.

If we have a function `y = f(x1, x2, ..., xn)`

the partial derivative with respect to argument `xi`

is defined as follows:

## Higher-order derivatives

We can also take derivatives and partial derivatives of **higher orders**. For example, the second (partial) derivative is defined as the (partial) derivative of the first (partial) derivative of a function, and so on:

We can use `sympy`

library to calculate derivative of the second order too:

We used `d2f_dx2 = sp.diff(f, x, 2)`

to calculate the derivative of the second order of the function `f`

with respect to argument `x`

.

Everything was clear?