AP Calculus 3.2 Basic Differentiation Rules Objective: Know and apply the basic rules of differentiation Constant Rule Power Rule Sum and Difference Rule.

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Presentation transcript:

AP Calculus 3.2 Basic Differentiation Rules Objective: Know and apply the basic rules of differentiation Constant Rule Power Rule Sum and Difference Rule Sine/ Cosine Rule Natural Exponential Rule

Review What is the definition of a derivative?definition Use the definition to find the derivative of the function y = 3x 3 – 4x 2 + 9x – 5. Write the equation of the line tangent to y = 7x at the point (2, 33).

The Constant Rule Given the line y = 3, what is the slope? Given the line f(x) = - 10, what is the slope? Theorem: The derivative of a constant function is 0.

Power Rule

Constant Multiple Rule

Sum and Difference Rule

Derivatives of Sine and Cosine Graph y = sin x from 0 to 2π. y’ = Graph y = cos x from 0 to 2π. y’ =

Natural Exponential Function

Practice Problems Find the derivative of the following functions. 1.y = 7 2.f(x) = x 3 – 4x y = 2/x 4.f(t) = 4t 2 /5 5.y = 2cos x 6.f(x) = x + sin x 7.y = sin x - e x

Assignment 3.2 page 1365 – 65 by 5