3.9: Derivatives of Exponential and Logarithmic Functions.

Slides:

Advertisements

Similar presentations

3.2 Inverse Functions and Logarithms 3.3 Derivatives of Logarithmic and Exponential functions.

Advertisements

Basic Derivatives The Math Center Tutorial Services Brought To You By:

The Derivative. Definition Example (1) Find the derivative of f(x) = 4 at any point x.

3.1 Derivative of a Function

Calculus Chapter 5 Day 1 1. The Natural Logarithmic Function and Differentiation The Natural Logarithmic Function- The number e- The Derivative of the.

3.9: Derivatives of Exponential and Logarithmic Functions Mt. Rushmore, South Dakota Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie.

Common and Natural Logarithms. Common Logarithms A common logarithm has a base of 10. If there is no base given explicitly, it is common. You can easily.

The derivative as the slope of the tangent line

Chapter 3.4 Properties of Log Functions Learning Target: Learning Target: I can find the inverses of exponential functions, common logarithms (base 10),

MAC 1105 Section 4.3 Logarithmic Functions. The Inverse of a Exponential Function 

3.9: Derivatives of Exponential and Log Functions Objective: To find and apply the derivatives of exponential and logarithmic functions.

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.

AP Calculus Chapter 2, Section 2 Basic Differentiation Rules and Rates of Change

Ch 4 - Logarithmic and Exponential Functions - Overview

Turn in your Quiz!!! Complete the following:. Section 11-5: Common Logarithms The questions are… What is a common log? How do I evaluate common logs?

Chapter 4 Techniques of Differentiation Sections 4.1, 4.2, and 4.3.

3.9: Derivatives of Exponential and Logarithmic Functions.

3.9 Exponential and Logarithmic Derivatives Thurs Oct 8

NATURAL LOGARITHMS. The Constant: e e is a constant very similar to π. Π = … e = … Because it is a fixed number we can find e 2.

7.4 Logarithmic Functions Write equivalent forms for exponential and logarithmic equations. Use the definitions of exponential and logarithmic functions.

Logarithmic, Exponential, and Other Transcendental Functions

STANDARD: STUDENTS SHOULD BE ABLE TO USE DERIVATIVES TO SOLVE A VARIETY OF PROBLEMS OBJECTIVE: DERIVE AND APPLY THE DERIVATIVE OF A LOGARITHM Agenda:

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.

3.9: Derivatives of Exponential and Logarithmic Functions.

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.

Logarithmic Functions Mrs. White Algebra II. What are logarithms? The inverse of the exponential function!

Common Logarithms - Definition Example – Solve Exponential Equations using Logs.

Logarithmic Functions. Examples Properties Examples.

Derivatives of Exponential and Inverse Trig Functions Objective: To derive and use formulas for exponential and Inverse Trig Functions.

Derivatives of Logarithmic Functions Objective: Obtain derivative formulas for logs.

Derivatives. Product Rule Quotient Rule The Chain Rule.

Goals:  Understand logarithms as the inverse of exponents  Convert between exponential and logarithmic forms  Evaluate logarithmic functions.

The Natural Exponential Function. Definition The inverse function of the natural logarithmic function f(x) = ln x is called the natural exponential function.

Section 5.4 Exponential Functions: Differentiation and Integration.

AP Calculus 3.2 Basic Differentiation Rules Objective: Know and apply the basic rules of differentiation Constant Rule Power Rule Sum and Difference Rule.

Algebra The Natural Base, e. Review Vocabulary Exponential Function–A function of the general form f(x) = ab x Growth Factor – b in the exponential.

Basic Derivatives Brought To You By: Tutorial Services The Math Center.

Derivatives of Logarithmic Functions

Derivatives of exponentials and Logarithms

AP Calculus BC September 12, 2016.

Logarithmic Functions and Their Graphs

Exponential and Logarithmic Functions

Warm up: Below is a graph of f(x). Sketch the graph of f’(x)

3.9: Derivatives of Exponential and Logarithmic Functions, p. 172

3 Exponential and Logarithmic Functions

Derivative of a Function

Derivatives of Exponential and Logarithmic Functions

Common and Natural Logarithms

Sec 3.1: DERIVATIVES of Polynomial and Exponential

Warm Up Six Chapter 5.5 Derivatives of base not e 11/20/2018

Logarithmic Functions and Their Graphs

Derivatives of Logarithmic Functions

Logarithms and Logarithmic Functions

Simplifying Logarithms

Simplifying Logarithms

3.9: Derivatives of Exponential and Logarithmic Functions

Warmup Solve 256

Exponential and Logarithmic Derivatives

Some of the material in these slides is from Calculus 9/E by

Limits, continuity, and differentiability computing derivatives

3.4 Exponential and Logarithmic Equations

Exponential and Logarithmic Functions

3.9: Derivatives of Exponential and Logarithmic Functions

Derivatives of Exponential and Logarithmic Functions

Exponential and Logarithmic Functions

L8-3 Obj: Students will use definition of log

3.9: Derivatives of Exponential and Logarithmic Functions

6.3 Logarithmic Functions

Packet #13 Exponential and Logarithmic Functions Math 160 Packet #13 Exponential and Logarithmic Functions.

3.7: Derivatives of Exponential and Logarithmic Functions

Presentation transcript:

3.9: Derivatives of Exponential and Logarithmic Functions

Look at the graph of If we assume this to be true, then: The slope at x=0 appears to be 1. definition of derivative

Now we attempt to find a general formula for the derivative of using the definition. This is the slope at x=0, which we have assumed to be 1.

is its own derivative! If we incorporate the chain rule: We can now use this formula to find the derivative of

( and are inverse functions.) (chain rule)

( is a constant.) Incorporating the chain rule:

So far today we have: Now it is relatively easy to find the derivative of .

To find the derivative of a common log function, you could just use the change of base rule for logs: The formula for the derivative of a log of any base other than e is:

p

Homework: 3.9a 3.9 p178 3,12,21,30,39 3.8 p170 24,41 2.4 p92 11,29 3.9b 3.9 p178 6,15,24,27,33,42,49,55,64

Review: p181 3-75 multiples of 3 (practice test – extra credit) TEST: Ch. 3 & 2