3.5 Derivatives of Trig Functions

Slides:



Advertisements
Similar presentations
Consider the function We could make a graph of the slope: slope Now we connect the dots! The resulting curve is a cosine curve. 2.3 Derivatives of Trigonometric.
Advertisements

3.5 Derivatives of Trig Functions. Consider the function We could make a graph of the slope: slope Now we connect the dots! The resulting curve is a cosine.
Calculus Warm-Up Find the derivative by the limit process, then find the equation of the line tangent to the graph at x=2.
Derivatives of Powers and Polynomials Colorado National Monument Greg Kelly, Hanford High School, Richland, Washington Adapted by: Jon Bannon Siena College.
Y x z An Introduction to Partial Derivatives Greg Kelly, Hanford High School, Richland, Washington.
Consider the function We could make a graph of the slope: slope Now we connect the dots! The resulting curve is a cosine curve.
Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2001 London Bridge, Lake Havasu City, Arizona 2.3 Product and Quotient Rules.
Consider the function We could make a graph of the slope: slope Now we connect the dots! The resulting curve is a cosine curve.
Product rule: Notice that this is not just the product of two derivatives. This is sometimes memorized as:
Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2001 London Bridge, Lake Havasu City, Arizona 3.4 Derivatives of Trig Functions.
Bell-ringer 11/2/09 Suppose that functions f and g and their derivatives with respect to x have the following values at x=0 and x=1. 1.Evaluate the derivative.
Hypatia of Alexandria 370 – 415 Hypatia of Alexandria 370 – 415 Hypatia was an Alexandrine Greek Neoplatonist philosopher in Egypt who was one of the earliest.
Greg Kelly, Hanford High School, Richland, Washington Adapted by: Jon Bannon Siena College Photo by Vickie Kelly, 2001 London Bridge, Lake Havasu City,
2.3 Basic Differentiation Formulas
3.5 Implicit Differentiation
2.3 The Product and Quotient Rules (Part 1)
London Bridge, Lake Havasu City, Arizona
2.4 Rates of Change and Tangent Lines
Derivatives of Trig Functions
Mean Value Theorem for Derivatives
2.3 Basic Differentiation Formulas
8.2 Derivatives of Inverse Trig Functions
3.6 part 2 Derivatives of Inverse Trig Functions
Colorado National Monument
Differentiation Rules
2.1 The Derivative and the Tangent Line Problem (Part 2)
3.4 Derivatives of Trig Functions
London Bridge, Lake Havasu City, Arizona
Derivatives of Trig Functions
Derivatives of Trig Functions
Derivatives of Trig Functions
Mark Twain’s Boyhood Home
Mark Twain’s Boyhood Home
Derivatives of Inverse Trig Functions
3.2 Differentiability Arches National Park - Park Avenue
3.6 The Chain Rule Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2002.
3.3 Differentiation Rules
3.8 Derivatives of Inverse Trig Functions
Black Canyon of the Gunnison National Park, Colorado
5.2 (Part I): The Natural Logarithmic Function and Integration
Black Canyon of the Gunnison National Park, Colorado
3.6 The Chain Rule Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2002.
Rates of Change and Tangent Lines
The Tangent and Velocity Problems
3.9: Derivatives of Exponential and Logarithmic Functions
3.8 Derivatives of Inverse Trig Functions
3.3 Differentiation Rules
Rules for Differentiation
2.4 Rates of Change and Tangent Lines
2.2 Basic Differentiation Rules and Rates of Change (Part 1)
5.7 Inverse Trig Functions and Integration (part 2)
Colorado National Monument
3.4 Derivatives of Trig Functions
3.3 Rules for Differentiation
2.4 The Chain Rule (Part 2) Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2002.
2.2 Basic Differentiation Rules and Rates of Change (Part 1)
3.5 The Chain Rule Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2002.
8.2 Day 2: Identifying Indeterminate Forms
An Introduction to Partial Derivatives
3.3 Differentiation Rules
3.7 Implicit Differentiation
3.9: Derivatives of Exponential and Logarithmic Functions
5.2 (Part I): The Natural Logarithmic Function and Integration
3.5 Derivatives of Trig Functions
Parametric Functions 10.1 Greg Kelly, Hanford High School, Richland, Washington.
3.3 Differentiation Rules
2.1 The Derivative and the Tangent Line Problem (Part 2)
3.7: Derivatives of Exponential and Logarithmic Functions
2.5 Basic Differentiation Properties
London Bridge, Lake Havasu City, Arizona
Presentation transcript:

3.5 Derivatives of Trig Functions London Bridge, Lake Havasu City, Arizona Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2001

Consider the function slope We could make a graph of the slope: Now we connect the dots! The resulting curve is a cosine curve.

We can do the same thing for slope The resulting curve is a sine curve that has been reflected about the x-axis.

We can find the derivative of tangent x by using the quotient rule.

Derivatives of the remaining trig functions can be determined the same way. p