## 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: 

import sympy as sp

# Define the variables
x, y = sp.symbols('x y')

# Define the function
f = x**3 + 2*x*y + y**2 + x - 3*y

# Calculate the partial derivative with respect to x
df_dx = sp.diff(f, x)

# Calculate the partial derivative with respect to y
df_dy = sp.diff(f, y)

# Define the point at which to evaluate the partial derivatives
point = {x: 2, y: 3}

# Evaluate the partial derivatives at the given point
df_dx_value = df_dx.subs(point)
df_dy_value = df_dy.subs(point)

# Print the partial derivatives
print(f'Partial derivative with respect to x: {df_dx}')
print(f'Partial derivative with respect to y: {df_dy}')

# Print the partial derivatives at the given point
print(f'Partial derivative with respect to x at point {point}: {df_dx_value}')
print(f'Partial derivative with respect to y at point {point}: {df_dy_value}')

## 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:

import sympy as sp

# Define the variable
x, y = sp.symbols('x y')

# Define the function
f = 2*x**3 + sp.sin(x*y)

# Calculate the second-order derivative
d2f_dx2 = sp.diff(f, x, 2)

# Print the second-order derivative
print(f'Second-order partial derivative with respect to x is: {d2f_dx2}')

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`.

To study many applied disciplines, it is necessary to have basic knowledge of higher mathematics and linear algebra. Mathematics is often used in data analysis, system modeling, building machine learning models, etc. Let's look at some of the most important topics and learn how to use the mathematical apparatus to solve real problems.

Let's start with some basic definitions and concepts we'll use later. Consider the idea of a function, a numerical sequence, and its sum, and also understand what a coordinate system's basis is.

The simplest and most commonly used type of relationship is the linear relationship. Linear algebra is a branch of higher mathematics entirely devoted to linear functions and linear spaces. Let's look at some of the most important topics in linear algebra: vectors, matrices, solving linear equations, and solving the spectral problem for matrices.

Mathematical analysis is a discipline that allows you to analyze functions according to various criteria. Consider how to check numerical sequences for convergence, find the maximum/minimum values of functions, solve nonlinear equations, and use integrals to solve applied problems.

Mathematics for Data Analysis and Modeling

Partial Derivative of the Function

Partial derivative

Higher-order derivatives