Basic Differentiation Rules The CONSTANT Rule: The derivative of a constant function is 0.

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Presentation transcript:

Basic Differentiation Rules The CONSTANT Rule: The derivative of a constant function is 0.

Basic Differentiation Rules The POWER Rule: In the case of n = 1, the power rule is best thought of as a separate differentiation rule.

Basic Differentiation Rules The POWER Rule: Example:

Basic Differentiation Rules The Constant Multiple Rule: Example:

Basic Differentiation Rules The Sum and Difference Rule: Example:

Basic Differentiation Rules The derivative of Sine and Cosine: Example:

Rates of Change A function s that gives the position of an object as a function of time t is called a position function. Knowing that, the Average Velocity is

Rates of Change - Example

Rates of Change What if we wanted to know the velocity at a specific time instead of the average velocity over an extended amount of time? The instantaneous velocity is the derivative of the position function. Note: Velocity can be negative, zero or positive. The speed is the absolute value of its velocity.

Rates of Change - Example