2.5 Implicit Differentiation

Slides:

Advertisements

Similar presentations

Equations of Tangent Lines

Advertisements

The Derivative and the Tangent Line Problem. Local Linearity.

Find the slope of the tangent line to the graph of f at the point ( - 1, 10 ). f ( x ) = 6 - 4x

Derivative Review Part 1 3.3,3.5,3.6,3.8,3.9. Find the derivative of the function p. 181 #1.

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.

Implicit Differentiation

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.

Differentiation Jeopardy Power RuleProduct RuleQuotient.

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

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

Aim: What Is Implicit Differentiation and How Does It Work?

Implicit Differentiation

3.1 –Tangents and the Derivative at a Point

Implicit Differentiation 3.6. Implicit Differentiation So far, all the equations and functions we looked at were all stated explicitly in terms of one.

Differentiation Copyright © Cengage Learning. All rights reserved.

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

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.

Ms. Battaglia AB/BC Calculus. Up to this point, most functions have been expressed in explicit form. Ex: y=3x 2 – 5 The variable y is explicitly written.

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.

AP Calculus AB Chapter 2, Section 5 Implicit Differentiation

3.2 & 3.3. State the Differentiability Theorem Answer: If a function is differentiable at x=a, then the function is continuous at x=a.

GOAL: USE DEFINITION OF DERIVATIVE TO FIND SLOPE, RATE OF CHANGE, INSTANTANEOUS VELOCITY AT A POINT. 3.1 Definition of Derivative.

Copyright © Cengage Learning. All rights reserved.

Implicit Differentiation Objective: To find derivatives of functions that we cannot solve for y.

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.

You can do it!!! 2.5 Implicit Differentiation. How would you find the derivative in the equation x 2 – 2y 3 + 4y = 2 where it is very difficult to express.

2.1 The Derivative and the Tangent Line Problem.

DO NOW: Find the inverse of: How do you find the equation of a tangent line? How do you find points where the tangent line is horizontal?

Aim: How do we take second derivatives implicitly? Do Now: Find the slope or equation of the tangent line: 1)3x² - 4y² + y = 9 at (2,1) 2)2x – 5y² = -x.

Slide Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

AP Calculus BC September 12, 2016.

6.1 – 6.3 Differential Equations

Implicit Differentiation

Copyright © Cengage Learning. All rights reserved.

Implicit Differentiation

2.6 Implicit Differentiation

4.2 – Implicit Differentiation

Section 3.7 Implicit Functions

Chain Rules for Functions of Several Variables

2.5 Implicit Differentiation

Implicit Differentiation

Chain Rules for Functions of Several Variables

MTH1170 Implicit Differentiation

Implicit Differentiation Implicit differentiation

Copyright © Cengage Learning. All rights reserved.

Problem of the Day (Calculator Allowed)

4.2 – Implicit Differentiation

Implicit Differentiation

Implicit Differentiation

The Derivative and the Tangent Line Problems

Implicit Differentiation

Implicit Differentiation

Part (a) Keep in mind that dy/dx is the SLOPE! We simply need to substitute x and y into the differential equation and represent each answer as a slope.

Implicit Differentiation

Implicit Differentiation

Calculus Implicit Differentiation

Implicit Differentiation

Implicit Differentiation

Implicit Differentiation

IMPLICIT Differentiation.

Implicit Differentiation & Related Rates

Copyright © Cengage Learning. All rights reserved.

Copyright © Cengage Learning. All rights reserved.

7. Implicit Differentiation

More with Rules for Differentiation

Copyright © Cengage Learning. All rights reserved.

Presentation transcript:

2.5 Implicit Differentiation

Differentiating with Respect to x Variables don’t match Variables match

Differentiating with Respect to x

Implicit Differentiation Find dy/dx given that

Finding the slope of a graph implicitly Determine the slope of the tangent line to the graph of at the point

Finding the slope of a graph implicitly Determine the slope of the graph of at the point (3,1).

Finding the Second Derivative Implicitly Given , find

Finding a tangent line to a graph Find the tangent line to the graph given by at the point