## Differentiation of real functions of one and several variables

### Teaching unit

### Description

Calculation of derivatives of functions of one or two variables.

### Objectives

Acquire and use mathematical language fluently, both orally and in writing, and rigorous formalization and structuring of a real problem in the form of mathematical problem.

To know how to compose functions and derive composite functions by chain rule.

Recognize homogeneous functions and calculate the degree of homogeneity.

Ability to apply knowledge, methods and algorithms to situations and problems in the area of economic enterprise.

Correctly handle the literature and information sources available to strengthen and expand knowledge and increase torque capacity to pose and solve mathematical so many problems that may arise and relate to the subject.

Use various technological tools (such as computer software) that facilitate solving math problems and understand the limitations of such tools.

Knowledge and skill in handling major real functions of real variable linear, quadratic, polynomial, rational, trigonometric, exponential, logarithmic. Being able to use them as a tool to solve a large variety of problems.

Understand the concept of derivative of a function and its economic interpretation.

Calculate derivatives of functions of several variables, both first order and higher orders. Use them to solve optimization problems.

### Subjects

#### Lecture topics

- Derivatives of functions of one variable.
- Partial derivatives of scalar functions.
- Differential of a function of several variables.
- Differentiation of composite functions.
- Homogeneous functions. Euler's theorem.
- Partial elasticities.

#### Laboratory topics

- Study and representation of functions of one variable.
- Successive derivatives of functions of one or several variables. Gradients, Jacobians and Hessian matrix.
- Chain rule
- Homogeneity of functions. Partial elasticities.