Basic Differentiation Rules and Rate of Change

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Presentation transcript:

Basic Differentiation Rules and Rate of Change Section 2.2 Basic Differentiation Rules and Rate of Change

Overview 4 Basic Rules Trig Rules (sine and cosine) Average and Instantaneous rates of change

Rule 1: Constant Rule Function Derivative

Rule 2: Power Rule Function Work Derivative

Rule 3: Constant Multiple Function Work Derivative

Rule 4: Sum and Difference Function Work Derivative

Trig Derivatives

Rates of Change: Average and Instantaneous Velocity

(b, s(b)) (a, s(a))

We need to find the slope of the tangent line when t=a. (b, s(b)) (b, s(b)) (a, s(a)) We need to find the slope of the tangent line when t=a.

Ex: At t=0, a diver jumps off of the high dive platform from 32 ft above the water. The diver’s initial velocity is 16 ft/s. Write the position function of the diver When does the diver hit the water? What is the diver’s velocity at impact?