Differential Calculus

La duración total del curso es de 3 horas.

1. Introduction.
   • Overview of differentiation and its importance in calculus.
   • Introduction to the concept of a derivative and its applications.
2. Derivarives of polynomials an anatural exponential functions.
   • Finding derivatives of polynomial functions using power rule.
   • Derivatives of exponential functions like exe^xex and their applications.
3. The product rule.
   • Statement and proof of the product rule.
   • Application of the product rule to find derivatives of products of functions.
4. The quotient rule.
   • Statement and derivation of the quotient rule.
   • Understanding when and how to apply the quotient rule.
5. Derivatives of trigonometric functions.
   • Derivatives of basic trigonometric functions (sin, cos, tan).
   • Derivatives of trigonometric identities and compositions.
6. The chain rule.
   • Statement and application of the chain rule for composite functions.
7. Implicit differentiation
   • Introduction to implicit differentiation and its purpose.
   • Applying implicit differentiation to find derivatives of implicitly defined functions.
8. Derivatives of inverse trigonometric functions.
   • Derivatives of inverse trigonometric functions (arcsin, arccos, arctan).
   • Solving problems involving derivatives of inverse trigonometric identities.
9. Derivatives of logrihmic functions.
   • Derivatives of logarithmic functions and their properties.
   • Using logarithmic differentiation to find derivatives of complicated functions.
10. Logarthmic differentiation.
    • Understanding the concept and process of logarithmic differentiation.
    • Applying and examples of logarithmic differentiation.

1. Conocimiento sólido en álgebra, incluyendo Álgebra I y Álgebra II.
2. Familiaridad con Geometría y habilidades básicas en trigonometría.
3. Haber cursado un curso de Precálculo o tener conocimientos equivalentes.
4. Comprensión básica de funciones y gráficos.
5. Dominio de las operaciones con exponentes y logaritmos.

La realización del curso será completamente on-line y evaluado a través de un examen. Una vez superado el mismo, podrás recibir tu título, válido para toda España.

Una vez hayas completado el curso, puede realizar el test relacionado y obtener tu título.