'Implicit differentiation' diaporamas de présentation

Implicit Differentiation

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2.5 Implicit Differentiation

2.5 Implicit Differentiation. Implicit DIfferentiation.

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

Aim: What Is Implicit Differentiation and How Does It Work?. Implicit. Do Now:. Explicit. Explicit Form . Implicit Form. Often you can solve for y in term of x. Implicit vs. Explicit. variable y is written as a function of x. derivative of y ?. Not Always!.

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2014 Implicit Differentiation

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Introduction

Introduction. We will cover 4 topics today 1. Gradient of a Slope 2. Rates of Change 3. Important Derivatives 4. Higher Order Derivatives. The Gradient of a Slope. y. y. q. q. q. dy. p. p. dx. tangent. x. x.

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Do Now

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Implicit Differentiation

Implicit Differentiation. The functions that we have met so far can be described by expressing one variable explicitly in terms of another variable. For example, , or y = x sin x , or in general y = f ( x ). However, some functions are defined implicitly.

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Simpsons Rule

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Implicit Differentiation

Implicit Differentiation. Lesson 3.5. Introduction. Consider an equation involving both x and y: This equation implicitly defines a function in x It could be defined ex plicitly. Differentiate. Differentiate both sides of the equation each term one at a time

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3.7 Implicit Differentiation

3.7 Implicit Differentiation. Niagara Falls, NY & Canada. Photo by Vickie Kelly, 2003. Greg Kelly, Hanford High School, Richland, Washington. F4. F3. 2. On the sending unit, press , and then . . 2nd. VAR-LINK. 2nd.

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3.7 Implicit Differentiation

3.7 Implicit Differentiation. Niagara Falls, NY & Canada. Photo by Vickie Kelly, 2003. Greg Kelly, Hanford High School, Richland, Washington. F4. F3. 2. On the sending unit, press , and then . . 2nd. VAR-LINK. 2nd.

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Using implicit differentiation: Related rate problems

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The trouble with isolating y...

The trouble with isolating y. Is the relation y = x 3 + x a function? Justify your answer. Is the inverse of the above relation a function? Again, justify!. Graph:. Equation:. (Erase). Is y a function of x ?. Can we isolate the dependent variable?.

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Calculus Section 5.4 Differentiate logarithmic functions

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3.5 Inverse Trigonometric Functions

3.5 Inverse Trigonometric Functions. Inverse sine (or arcsine) function. f(x)=sin x is not one-to-one

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Sec 15.4 Tangent Planes and Linear Approximations

Sec 15.4 Tangent Planes and Linear Approximations. Suppose f has continuous partial derivatives. An equation of the tangent plane to the surface z = f ( x , y ) at the point The linear function: whose graph is the tangent plane at the point ( a, b ) is called

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