Derivative Rules and Formulas
This page provides a comprehensive overview of derivative formulas and rules, essential for students studying calculus. The content is organized into sections covering different types of functions and operations.
The page begins by introducing the concept of a fonction dérivée (derivative function). It then proceeds to list various derivative rules for common mathematical operations and functions.
Definition: The derivative of a function represents the rate of change of the function at any given point.
For basic operations, the following rules are presented:
- Derivative of a sum: (u + v)' = u' + v'
- Derivative of a product: (u × v)' = u'v + v'u
Example: The derivative of f(x) = x² is f'(x) = 2x, illustrating the power rule for derivatives.
The page also includes more complex derivative formulas:
- Derivative of a quotient: (u/v)' = (u'v - v'u) / v²
- Derivative of a constant: (k)' = 0
- Power rule: (x^n)' = nx^(n-1)
- Derivative of square root: (√x)' = 1 / (2√x)
Highlight: The power rule is a fundamental concept in calculus, allowing for the quick derivation of polynomial functions.
At the bottom of the page, the equation for the tangent line to a function at a specific point is provided:
Formula: y = f'(a)(x - a) + f(a)
This equation is crucial for understanding the geometric interpretation of derivatives and their applications in finding slopes of tangent lines.
Vocabulary:
- Tangent: A line that touches a curve at a single point without crossing it.
- Dérivée: The French term for derivative.
This comprehensive summary of derivative formulas serves as an excellent resource for students preparing for exams or seeking to reinforce their understanding of calculus concepts.
