Comprehensive Guide to Derivatives
This page presents a detailed Tableau des dérivées usuelles and Tableau dérivée fonction composée, providing students with a valuable resource for calculus studies. The table is divided into two main sections: basic function derivatives and derivative rules for operations on functions.
The first section of the table focuses on fundamental functions and their derivatives:
Highlight: The table begins with the simplest case: the derivative of a constant (k) is always 0.
Following this, it lists the derivatives of power functions:
Example: For x², the derivative is 2x, and for x³, it's 3x².
Vocabulary: The term "nx^(n-1)" represents the general form for the derivative of x^n, where n is any real number.
The table also includes the derivative of the square root function:
Definition: The derivative of √x is 1/(2√x).
The second part of the table covers Opérations sur les fonctions dérivées, detailing rules for more complex operations:
- Sum Rule: (u + v)' = u' + v'
- Constant Multiple Rule: (ku)' = ku'
- Product Rule: (uv)' = u'v + uv'
- Quotient Rule: (u/v)' = (u'v - uv')/v²
- Power Rule: (u^n)' = nu^(n-1)u'
Highlight: These rules are essential for solving more complex derivative problems and are widely used in Fonction dérivée exercice corrigé.
The table also provides information on the intervals of definition for each function, ensuring students understand the domain restrictions for certain operations.
Quote: "INTERVALLE R" indicates that the function is defined for all real numbers, while "R*" excludes zero from the domain.
This comprehensive Tableau des dérivées PDF serves as an invaluable tool for students tackling derivatives, from basic functions to more advanced composite functions and operations.
