Implicit Differentiation

Slides:



Advertisements
Similar presentations
The Natural Logarithmic Function
Advertisements

Warm Up Sketch the graph of y = ln x What is the domain and range?
3.2 Inverse Functions and Logarithms 3.3 Derivatives of Logarithmic and Exponential functions.
Point Value : 20 Time limit : 2 min #1 Find. #1 Point Value : 30 Time limit : 2.5 min #2 Find.
However, some functions are defined implicitly. Some examples of implicit functions are: x 2 + y 2 = 25 x 3 + y 3 = 6xy.
DIFFERENTIATION & INTEGRATION CHAPTER 4.  Differentiation is the process of finding the derivative of a function.  Derivative of INTRODUCTION TO DIFFERENTIATION.
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.
Solving Equations = 4x – 5(6x – 10) -132 = 4x – 30x = -26x = -26x 7 = x.
Exponential and Logarithmic Functions 5 Exponential Functions Logarithmic Functions Differentiation of Exponential Functions Differentiation of Logarithmic.
2.5 Implicit Differentiation. Implicit and Explicit Functions Explicit FunctionImplicit Function But what if you have a function like this…. To differentiate:
Implicit Differentiation. Objectives Students will be able to Calculate derivative of function defined implicitly. Determine the slope of the tangent.
A) Find the velocity of the particle at t=8 seconds. a) Find the position of the particle at t=4 seconds. WARMUP.
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
The Natural Logarithmic Function
Implicit Differentiation
1 Implicit Differentiation Lesson Introduction Consider an equation involving both x and y: This equation implicitly defines a function in x It.
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.
1 Implicit Differentiation. 2 Introduction Consider an equation involving both x and y: This equation implicitly defines a function in x It could be defined.
Section 2.5 Implicit Differentiation
Homework questions? 2-5: Implicit Differentiation ©2002 Roy L. Gover ( Objectives: Define implicit and explicit functions Learn.
Objectives: 1.Be able to determine if an equation is in explicit form or implicit form. 2.Be able to find the slope of graph using implicit differentiation.
3.6 Derivatives of Logarithmic Functions In this section, we: use implicit differentiation to find the derivatives of the logarithmic functions and, in.
CHAPTER Continuity Implicit Differentiation.
Implicit Differentiation. Implicitly vs. Explicitly Defined Functions y is given explicitly as a function of x (y is solved in terms of x) y is given.
3.7 – Implicit Differentiation An Implicit function is one where the variable “y” can not be easily solved for in terms of only “x”. Examples:
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.
Logarithmic Differentiation
Implicit differentiation (2.5) October 29th, 2012.
CHAPTER 4 DIFFERENTIATION NHAA/IMK/UNIMAP. INTRODUCTION Differentiation – Process of finding the derivative of a function. Notation NHAA/IMK/UNIMAP.
Calculus and Analytical Geometry
Copyright © Cengage Learning. All rights reserved. 3 Differentiation Rules.
Implicit Differentiation 3.5. Explicit vs. Implicit Functions.
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.
1 3.6 – Derivatives of Logarithmic Functions. 2 Rules Why is the absolute value needed?
Chapter 3 Derivatives.
Copyright © Cengage Learning. All rights reserved.
Implicit Differentiation
Implicit Differentiation
Section 3.7 Implicit Functions
Implicit Differentiation
(8.2) - The Derivative of the Natural Logarithmic Function
MTH1170 Implicit Differentiation
CHAPTER 4 DIFFERENTIATION.
8.6 Solving Exponential & Logarithmic Equations
Sec 3.5: IMPLICIT DIFFERENTIATION
Implicit Differentiation Continued
Implicit Differentiation
2.5 Implicit Differentiation
Copyright © Cengage Learning. All rights reserved.
Implicit Differentiation
Implicit Differentiation
Derivatives of Logarithmic Functions
Implicit Differentiation
Copyright © Cengage Learning. All rights reserved.
Implicit Differentiation
Sec 3.6: DERIVATIVES OF LOGARITHMIC FUNCTIONS
Differentiate. f (x) = x 3e x
§ 4.6 Properties of the Natural Logarithm Function.
Implicit Differentiation
IMPLICIT DIFFERENTIATION
2.5 Implicit Differentiation
IMPLICIT Differentiation.
IMPLICIT DIFFERENTIATION
Presentation transcript:

Implicit Differentiation

Background In some cases it is not possible to solve an equation as a single equation For Example: would be solved as two equations: and In order to find the derivative of the function, you would have had to find the derivative of each part

Implicit Differentiation Don’t need to solve an equation for y first in order to find y’ You will differentiate both sides with respect to x and solve the result for y’

Example Find y’ for

Practice Find y’ for:

Find the derivatives at the given points:

Find the equation of the tangent line to the function at the given point:

Find the second derivative 7) 8) 9)

Logarithmic Differentiation Derivatives of complicated functions can be simplified by taking logarithms

Example Find the derivative of

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2024 SlidePlayer.com Inc. All rights reserved.