3.3 – Rules for Differentiation

Slides:

Advertisements

Similar presentations

Section 3.3a. The Do Now Find the derivative of Does this make sense graphically???

Advertisements

Derivatives - Equation of the Tangent Line Now that we can find the slope of the tangent line of a function at a given point, we need to find the equation.

Do Now Find the tangents to the curve at the points where

1.4 – Differentiation Using Limits of Difference Quotients

The Power Rule  If we are given a power function:  Then, we can find its derivative using the following shortcut rule, called the POWER RULE:

10.5 Basic Differentiation Properties. Instead of finding the limit of the different quotient to obtain the derivative of a function, we can use the rules.

If the derivative of a function is its slope, then for a constant function, the derivative must be zero. example: The derivative of a constant is zero.

Every slope is a derivative. Velocity = slope of the tangent line to a position vs. time graph Acceleration = slope of the velocity vs. time graph How.

By: Rafal, Paola, Mujahid.  y=e x (exponential function)  LOGARITHM FUNCTION IS THE INVERSE  EX1: y=log 4 xy=4 x  Therefore y=e x y=log e x.

Differentiation Formulas

If the derivative of a function is its slope, then for a constant function, the derivative must be zero. example: The derivative of a constant is zero.

Rules for Differentiation Colorado National Monument Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003.

3.3 Rules for Differentiation AKA “Shortcuts”. Review from places derivatives do not exist: ▫Corner ▫Cusp ▫Vertical tangent (where derivative is.

Techniques of Differentiation. I. Positive Integer Powers, Multiples, Sums, and Differences A.) Th: If f(x) is a constant, B.) Th: The Power Rule: If.

3.3: Rules of Differentiation Objective: Students will be able to… Apply the Power Rule, Sum and Difference Rule, Quotient and Product Rule for differentiation.

Objectives: 1.Be able to find the derivative using the Constant Rule. 2.Be able to find the derivative using the Power Rule. 3.Be able to find the derivative.

3.3 Rules for Differentiation What you’ll learn about Positive integer powers, multiples, sums, and differences Products and Quotients Negative Integer.

2.3 Differentiation Rules Colorado National Monument Larson, Hostetler, & Edwards.

4.2:Derivatives of Products and Quotients Objectives: Students will be able to… Use and apply the product and quotient rule for differentiation.

Differentiability Arches National Park- Park Avenue.

Objectives: 1.Be able to find the derivative using the Constant Rule. 2.Be able to find the derivative using the Power Rule. 3.Be able to find the derivative.

Objectives: 1.Be able to find the derivative of functions by applying the Product Rule. Critical Vocabulary: Derivative, Tangent Daily Warm-Up: Find the.

3.3 Product and Quotient Rule Fri Sept 25 Do Now Evaluate each 1) 2) 3)

3.3 Rules for Differentiation Colorado National Monument.

Ch. 4 – More Derivatives 4.1 – Chain Rule. Ex: Find the derivative of h(x) = sin(2x 2 ). –This is not a product rule problem because it has one function.

Sec. 3.3: Rules of Differentiation. The following rules allow you to find derivatives without the direct use of the limit definition. The Constant Rule.

Powerpoint Jeopardy Definition of Derivatives Basic Derivatives Equation of Tangent Line Product & Quotient Rule Chain Rule

DO NOW: Write each expression as a sum of powers of x:

4.2:DERIVATIVES OF PRODUCTS AND QUOTIENTS Objectives: To use and apply the product and quotient rule for differentiation.

Basic Rules of Derivatives Examples with Communicators Calculus.

3.3 Differentiation Rules Colorado National Monument Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003.

2.3 Basic Differentiation Formulas

Ch. 3 – Derivatives 3.3 – Rules for Differentiation.

Calculus Section 3.1 Calculate the derivative of a function using the limit definition Recall: The slope of a line is given by the formula m = y 2 – y.

Shortcuts for Derivatives

§ 4.2 The Exponential Function e x.

Bell Ringer Solve even #’s.

Rules for Differentiation

3-3 rules for differentiation

Ch. 2 – Limits and Continuity

Ch. 11 – Limits and an Introduction to Calculus

Objectives for Section 11.3 Derivatives of Products and Quotients

Derivative Rules 3.3.

The Quotient Rule The Quotient Rule is used to find derivatives for functions written as a fraction:

3.1 Polynomial & Exponential Derivatives

2.3 Basic Differentiation Formulas

3.3 Rules for Differentiation

3.1 – Derivative of a Function

3.1 – Derivative of a Function

Differentiating Polynomials & Equations of Tangents & Normals

2.2 Rules for Differentiation

3.2: Rules for Differentiation

Differentiation Rules

3.3 Differentiation Rules

Lesson 3.3: Rules for Differentiability

Differentiation Rules

Daily Warm-Up: Find the derivative of the following functions

(This is the slope of our tangent line…)

3.3 Differentiation Rules

Rules for Differentiation

2.2 Basic Differentiation Rules and Rates of Change (Part 1)

3.3 Rules for Differentiation

2.2 Basic Differentiation Rules and Rates of Change (Part 1)

Section 2 – Derivatives and Antiderivatives

3.3 Differentiation Rules

Basic Rules of Differentiation

3.3 Differentiation Rules

2.5 Basic Differentiation Properties

Chapter 3 Additional Derivative Topics

Presentation transcript:

3.3 – Rules for Differentiation Ch. 3 – Derivatives 3.3 – Rules for Differentiation

Let’s learn some shortcuts for finding derivatives! Power Rule: If , then Ex: If g(x)=x5, then g’(x)=5x4 . Ex: If h(x)=x-2, then h’(x)=-2x-3 . Constant Multiple Rule: Ex: If f(x)=3x2, then Sum and Difference Rule: Ex: If f(x)= x2+x , then

Derivative of a Constant: If f(x)=c, then f’(x)=0. Ex: Find the derivative of the following functions.

To find a second derivative, find the derivative of the derivative! Ex: Find the second derivatives of the following functions.

Ex: Find the equation of the tangent line to f(x)=3x2+4x-2 at x=1. We need a point and a slope… To find slope, evaluate the derivative at x=1! Now make an equation using (1,f(1)) as your point!

Ex: Find the x-values at which the tangent line to the curve of Ex: Find the x-values at which the tangent line to the curve of is horizontal. Horizontal tangent line means slope=0 Slope=0 means derivative=0, so find the zeros of the derivative! So

Product Rule: When two functions are multiplied together, we must use product rule to find the total derivative. Ex: Find the derivative of f(x)=(3x2-x)(4–x3). Separate the problem into two products, u=3x2-x and v=4-x3 ... Would you get the same answer if you multiplied out f(x) at the start, then differentiated? YES!

Quotient Rule: Low d high minus high d low...all over the square below! Ex: Find the derivative of f(x). Let u=3x3-2 and v=2x Would you get the same answer if you separated f into two fractions? YES!

Ex: A formula for relating pressure and volume for an ideal gas is listed below. Assuming n, R, and T are constants, find dP/dV. We are differentiating w/respect to V! Treat n, R, and T as if they were constant numbers!