Rules for Differentiation

Slides:

Advertisements

Similar presentations

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

Advertisements

2.3 Rules for Differentiation Colorado National Monument Vista High, AB Calculus. Book Larson, V9 2010Photo by Vickie Kelly, 2003.

U2 L8 Chain and Quotient Rule CHAIN & QUOTIENT RULE

The Chain Rule Section 3.6c.

Basic Skills in Higher Mathematics Robert Glen Adviser in Mathematics Mathematics 1(H) Outcome 3.

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.

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.

Chapter 3 Limits and the Derivative

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.

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.

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.

3.1 Definition of the Derivative & Graphing the Derivative

Definition of Derivative.  Definition   f‘(x): “f prime of x”  y‘ : “y prime” (what is a weakness of this notation?)  dy/dx : “dy dx” or, “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 Rules for Differentiation Colorado National Monument.

Antiderivatives. Indefinite Integral The family of antiderivatives of a function f indicated by The symbol is a stylized S to indicate summation 2.

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:

Chapter 17.2 The Derivative. How do we use the derivative?? When graphing the derivative, you are graphing the slope of the original function.

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.

Unit 2 Lesson #1 Derivatives 1 Interpretations of the Derivative 1. As the slope of a tangent line to a curve. 2. As a rate of change. The (instantaneous)

3.3 – Rules for Differentiation

Shortcuts for Derivatives

Bell Ringer Solve even #’s.

3-3 rules for differentiation

AP Calculus BC September 12, 2016.

Ch. 11 – Limits and an Introduction to Calculus

Chapter 10 Limits and the Derivative

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

3. Differentiation Rules

3. Differentiation Rules

3.3 Differentiation Rules

2.5 Basic Differentiation Properties

Chapter 3 Additional Derivative Topics

Presentation transcript:

Rules for Differentiation Calculus Topics Rules for Differentiation

The following symbols indicate the derivative of a function y=f(x) The following symbols indicate the derivative of a function y=f(x). THEY ALL MEAN THE SAME THING! Read as “y prime” “f prime” “dy dx” or “the derivative of y with respect to x” “df dx” “d dx of f at x” or “the derivative of f at x”

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.

Ex: Find the derivative 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!

Ex: Find the derivative of the following functions using the product rule.

Quotient Rule: Low d high less high d low...all over low-low! 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: Find the derivative of the following functions using the quotient rule.