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Section 3.5 (Part 1) - Implicit Differentiation

Notes on Implicit Differentiation
Course

Mathematics (Math 1225)

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Academic year: 2022/2023
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Virginia Polytechnic Institute and State University

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Section 3: Implicit Differentiation (Part 1)

Learning Goals

What are our learning goals for this section?

In previous sections, we found the derivative of explicit functions. Now we will learn how to find the slopes of the tangent lines to curves defined implicitly.

Implicit Differentiation

Suppose we have an implicit equation of a curve, in terms of variables x and y, and we wish to find dy dx

:

1.

2.

3.

Example 3

Consider the ellipse C given by x 2 6 +

y 2 2 +

x − y = 1

  1. Find a formula of the slope of the tangent line to C at any given point (x, y) on C.

  2. How many lines are tangent to the ellipse at x = −6? Find the equations of those tangent lines.

Example 4

Consider the curve ekxy 2 = 3 + kx + y, where k is a constant. Determine the value of k so that the normal line to the curve at x = 0 is parallel to the line 6y + x + 2 = 0.

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Section 3.5 (Part 1) - Implicit Differentiation

Course: Mathematics (Math 1225)

61 Documents
Students shared 61 documents in this course

University: Virginia Polytechnic Institute and State University

Was this document helpful?
Section 3.5: Implicit Differentiation (Part 1)
Learning Goals
What are our learning goals for this section?
1©Math 1225, Virginia Tech

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