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S = contains supplemental resources
Course: Calculus I
Topic: Derivatives
Subtopic: Implicit Differentiation

Overview

An implicit equation is one where there are x's and y's on both sides of the equation usually so intermingled that it is difficult to isolate the y, for example xy3=sin(x2y). To differentiate these equations requires a process called implicit differentiation which is the focus of today's lesson.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 2.6.1 Understand the difference between an equation written explicitly and one written implicitly
• 2.6.2 Know that the graphs of most curves given implicitly are non-functions (do not pass the vertical line test)
• 2.6.3 Implicitly differentiate to find dy/dx
• 2.6.4 Implicitly differentiate to find the second or third derivative of an implicit equation
• 2.6.5 Use mathematically correct notation and format when differentiating implicitly
• 2.6.6 Find the slope of the tangent line to a point that lies on an implicitly defined curve
• 2.6.7 Find the point(s) at which an implicitly defined curve has a horizontal or vertical tangent line

Terminology

Define: implicit equation, explicit equation, implicit differentiation

Text Notes

This is an important section to get down well especially before we move into related rate applications which require implicit differentiation to solve.

Supplemental Resources (optional)