Derivatives

The derivative of a function represents the rate of change of the function at any given point.

Definition

The derivative of a function with respect to is defined as:

This limit represents the instantaneous rate of change of the function at point .

Common Derivatives

Here are some common derivatives:

1. Power rule:
2. Exponential:
3. Trigonometric:

Applications

Derivatives have numerous applications in:

• Physics (velocity, acceleration)
• Economics (marginal cost, marginal revenue)
• Engineering (rates of change)
• Optimization problems