1 3.6 – Derivatives of Logarithmic Functions. 2 Rules Why is the absolute value needed?

Slides:

Advertisements

Similar presentations

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

Advertisements

Exponential and Logarithmic Functions 5 Exponential Functions Logarithmic Functions Differentiation of Exponential Functions Differentiation of Logarithmic.

5.1 The Natural Logarithmic Function: Differentiation AB and BC 2015.

Section 2.5 – Implicit Differentiation

Aim: Differentiating Natural Log Function Course: Calculus Do Now: Aim: How do we differentiate the natural logarithmic function? Power Rule.

The Derivative of a Logarithm. If f(x) = log a x, then Notice if a = e, then.

7.2The Natural Logarithmic and Exponential Function Math 6B Calculus II.

The exponential function occurs very frequently in mathematical models of nature and society.

Derivative of Logarithmic Function.

3.6 Derivatives of Logarithmic Functions 1Section 3.6 Derivatives of Log Functions.

Derivatives of Logarithmic Functions

How can one use the derivative to find the location of any horizontal tangent lines? How can one use the derivative to write an equation of a tangent line.

Unit 5: Modeling with Exponential & Logarithmic Functions Ms. C. Taylor.

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

Properties of Logarithms Product, Quotient and Power Properties of Logarithms Solving Logarithmic Equations Using Properties of Logarithms Practice.

Section 2.5 – Implicit Differentiation. Explicit Equations The functions that we have differentiated and handled so far can be described by expressing.

Example: Sec 3.7: Implicit Differentiation. Example: In some cases it is possible to solve such an equation for as an explicit function In many cases.

8.3-4 – Logarithmic Functions. Logarithm Functions.

3.6 Derivatives of Logarithmic Functions In this section, we: use implicit differentiation to find the derivatives of the logarithmic functions and, in.

Section 3.5 Implicit Differentiation 1. Example If f(x) = (x 7 + 3x 5 – 2x 2 ) 10, determine f ’(x). Now write the answer above only in terms of y if.

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

Logarithmic Differentiation

Properties of Logarithms log b (MN)= log b M + log b N Ex: log 4 (15)= log log 4 3 log b (M/N)= log b M – log b N Ex: log 3 (50/2)= log 3 50 – log.

CHAPTER 4 DIFFERENTIATION NHAA/IMK/UNIMAP. INTRODUCTION Differentiation – Process of finding the derivative of a function. Notation NHAA/IMK/UNIMAP.

Solving Logarithmic Equations

Calculus and Analytical Geometry

Logarithmic Functions. Examples Properties Examples.

3.5 – Implicit Differentiation

Derivatives of Exponential and Logarithmic Functions

7.2* Natural Logarithmic Function In this section, we will learn about: The natural logarithmic function and its derivatives. INVERSE FUNCTIONS.

Aim: What are the properties of logarithms? Do Now: Rewrite the following exponential form into log form 1.b x = A 2.b y = B HW:p.331 # 16,18,20,22,24,26,28,38,40,42,48,52.

Section 9.4 – Solving Differential Equations Symbolically Separation of Variables.

Copyright © Cengage Learning. All rights reserved.

Derivatives of Logarithmic Functions

Derivatives of exponentials and Logarithms

Solving Exponential and Logarithmic Equations

Section 3.7 Implicit Functions

Implicit Differentiation

CHAPTER 4 DIFFERENTIATION.

6.5 Applications of Common Logarithms

logb AB = logbbx + y Aim: What are the properties of logarithms?

Solving Absolute Value Equations

Techniques of Differentiation

Copyright © Cengage Learning. All rights reserved.

7.5 Exponential and Logarithmic Equations

Derivatives of Logarithmic Functions

5.5 Properties and Laws of Logarithms

Implicit Differentiation

Copyright © Cengage Learning. All rights reserved.

10. Derivatives of Log Functions

Implicit Differentiation

1.4 Solving Absolute-Value Equations

§ 4.6 Properties of the Natural Logarithm Function.

73 – Differential Equations and Natural Logarithms No Calculator

4.3 – Differentiation of Exponential and Logarithmic Functions

Differentiate the function: {image} .

1.4 Solving Absolute-Value Equations

Solving Absolute Value Equations

Copyright © Cengage Learning. All rights reserved.

Properties of Logarithmic Functions

Warm-Up #10 Solve and graph 5x -3 < 7 and 3x < 6

Solving Absolute Value Equations

Solving Absolute Value Equations

Using Properties of Logarithms

Solving Absolute Value Equations

Solving Absolute Value Equations

Logarithmic Functions

Solve the equations. 4 2

Derivatives of Logarithmic and Exponential functions

Solving Absolute Value Equations

Presentation transcript:

1 3.6 – Derivatives of Logarithmic Functions

2 Rules Why is the absolute value needed?

3 Rules

4 Try Theses: Basics Evaluate the following.

5 Try Theses Determine the first derivative of each of the following. Do only minor simplification.

6 Laws of Logarithms

7 Logarithmic Differentiation 1.Take the natural logarithms of both sides of an equation y = f(x). 2.Use the laws of logarithms to separate expressions. Be sure to create a single product or quotient on the right-hand side at this stage. 3.Differentiate implicitly with respect to x. 4.Solve the resulting equation for y′.

8 Examples Determine the first derivative of each of the following.

9 Try Theses Determine the first derivative of each of the following.