653 B
653 B
| id | title |
|---|---|
| mat-02-derivatives | Derivatives: definition and rules |
Derivatives
Derivative definition
The derivative at a point is the limit of the difference quotient.
Derivative rules
Key rules include:
- constant and power rule
- sum and product rule
- quotient rule
- chain rule
Derivatives of common functions
Examples:
- derivative of x^n
- derivative of sin x and cos x
- derivative of e^x and ln x
Tangent line approximation
A derivative gives the slope of the tangent line and supports local linear approximation.
Critical points
Critical points occur where the derivative is zero or undefined (within the domain).