Sec 3.1: DERIVATIVES of Polynomial and Exponential Example: Constant function.

Slides:



Advertisements
Similar presentations
More on Derivatives and Integrals -Product Rule -Chain Rule
Advertisements

11.1 An Introduction to Limits Lim f(x) = L as x  a x  a - is as x approaches a from the left x  a + is as x approaches a from the right In order for.
Arithmetic Sequences and Series Unit Definition Arithmetic Sequences – A sequence in which the difference between successive terms is a constant.
Exponents, Polynomials, and Polynomial Functions.
CHAPTER Continuity CHAPTER Derivatives of Polynomials and Exponential Functions.
10.1 – Exponents Notation that represents repeated multiplication of the same factor. where a is the base (or factor) and n is the exponent. Examples:
Notes Over 11.3 Geometric Sequences
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.
12.2 – Analyze Arithmetic Sequences and Series. Arithmetic Sequence: The difference of consecutive terms is constant Common Difference: d, the difference.
THE BEST CLASS EVER…ERRR…. PRE-CALCULUS Chapter 13 Final Exam Review.
Derivatives of polynomials Derivative of a constant function We have proved the power rule We can prove.
Calculus Section 2.2 Basic Differentiation Rules and Rates of Change.
AP Calculus Chapter 2, Section 2 Basic Differentiation Rules and Rates of Change
Math 3120 Differential Equations with Boundary Value Problems
Math 1304 Calculus I 2.5 – Continuity. Definition of Continuity Definition: A function f is said to be continuous at a point a if and only if the limit.
Differentiating exponential functions.
DIFFERENTIATING “COMBINED” FUNCTIONS ---PART I CONSTANT MULTIPLES, SUMS AND DIFFERENCES.
3.3 Rules for Differentiation. What you’ll learn about Positive Integer Powers, Multiples, Sums and Differences Products and Quotients Negative Integer.
Slide 3- 1 Rule 1 Derivative of a Constant Function.
Notes Over 11.2 Arithmetic Sequences An arithmetic sequence has a common difference between consecutive terms. The sum of the first n terms of an arithmetic.
Section 3.1 Derivatives of Polynomials and Exponential Functions  Goals Learn formulas for the derivatives ofLearn formulas for the derivatives of  Constant.
Math 1304 Calculus I 3.1 – Rules for the Derivative.
2.1 Rates of Change and Limits. What you’ll learn about Average and Instantaneous Speed Definition of Limit Properties of Limits One-Sided and Two-Sided.
Product & quotient rules & higher-order derivatives (2.3) October 17th, 2012.
3.3 Rules for Differentiation Quick Review In Exercises 1 – 6, write the expression as a power of x.
Chapter3: Differentiation DERIVATIVES OF TRIGONOMETRIC FUNCTIONS: Chain Rule: Implicit diff. Derivative Product Rule Derivative Quotient RuleDerivative.
Integrating Exponential Functions TS: Making decisions after reflection and review.
In this section, we will consider the derivative function rather than just at a point. We also begin looking at some of the basic derivative rules.
Differentiating “Combined” Functions ---Part I Constant Multiples, Sums and Differences.
Sec 3.3: Differentiation Rules Example: Constant function.
SAT Prep. Basic Differentiation Rules and Rates of Change Find the derivative of a function using the Constant Rule Find the derivative of a function.
Basic Differentiation Rules The CONSTANT Rule: The derivative of a constant function is 0.
Basic rules of differentiation Recall that all represent the derivative. All rules follow from the definition of the derivative.
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.
15 E Derivatives of Exponential Functions Look at the graph of The slope at x=0 appears to be 1. If we assume this to be true, then: definition of derivative.
Product and Quotient Rule Find the derivative of the function using the Product Rule Find the derivative of the function using the Quotient Rule Find the.
The Tangent Line The Secant Line. The Tangent Line The Secant Line.
Chapter 2 Differentiation. Copyright © Houghton Mifflin Company. All rights reserved.2 | 2 Tangent Line to a Graph.
12.3 – Analyze Geometric Sequences and Series. Geometric Sequence: Ratio of any term to the previous term is constant Common Ratio: Ratio each term is.
Section 4.7 Variation of Parameters. METHOD OF VARIATION OF PARAMETERS For a second-order linear equation in standard form y″ + Py′ + Qy = g(x). 1.Find.
Derivatives. Product Rule Quotient Rule The Chain Rule.
Basic Rules of Derivatives Examples with Communicators Calculus.
Note starter Scour your notes for when we used the limit process to find a derivative, then fill in the table. FunctionDerivative.
AP Calculus 3.2 Basic Differentiation Rules Objective: Know and apply the basic rules of differentiation Constant Rule Power Rule Sum and Difference Rule.
Basic derivation rules We will generally have to confront not only the functions presented above, but also combinations of these : multiples, sums, products,
Rules for Differentiation
3.1 Polynomial & Exponential Derivatives
Warm up: Below is a graph of f(x). Sketch the graph of f’(x)
AP Calculus Honors Ms. Olifer
Rules for Differentiation
Rules for Differentiation
Polynomials Monomials & Operations
Derivatives of Exponential and Logarithmic Functions
3.9: Derivatives of Exponential and Logarithmic Functions.
Sec 3.1: DERIVATIVES of Polynomial and Exponential
Essential Questions How do we use the Factor Theorem to determine factors of a polynomial? How do we factor the sum and difference of two cubes.
Exam2: Differentiation
Derivatives of Polynomials and Exponential Functions
(This is the slope of our tangent line…)
Differentiating “Combined” Functions ---Part I
4-7 Sequences and Functions
Divisibility Rules.
3.1 – Rules for the Derivative
Differentiating “Combined” Functions ---Part I
Divisibility Rules.
Exam2: Differentiation
Rules for Differentiation
Plan of the Day One-Question Quiz Score Chapter 1 Test
Sec 3.3: Derivatives Of Trigonometric Functions
Geometric Sequences and series
Presentation transcript:

Sec 3.1: DERIVATIVES of Polynomial and Exponential Example: Constant function

Example: The power Rule Sec 3.1: DERIVATIVES of Polynomial and Exponential

Example: The power Rule Example: Sec 3.1: DERIVATIVES of Polynomial and Exponential

Example: The constant multiple Sec 3.1: DERIVATIVES of Polynomial and Exponential

Example: The sum and differnce Rule Sec 3.1: DERIVATIVES of Polynomial and Exponential

Example: Derivative of exponential Definition of the number e Sec 3.1: DERIVATIVES of Polynomial and Exponential

Derivative of exponential Example: Sec 3.1: DERIVATIVES of Polynomial and Exponential

Second- and Higher-Order Derivatives Example: First derivative second derivative 3ed derivative n-th derivative Sec 3.1: DERIVATIVES of Polynomial and Exponential

TERM-121 Exam-2 Sec 3.1: DERIVATIVES of Polynomial and Exponential

TERM-121 Exam-2 Sec 3.1: DERIVATIVES of Polynomial and Exponential

TERM-121 Exam-2 Sec 3.1: DERIVATIVES of Polynomial and Exponential