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Derivative implicit functions

Derivative implicit functions preview
Derivative implicit functions preview
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Opening slide for the implicit differentiation lesson, stating the objective: differentiate implicit functions
Lesson title and learning objective
Review slide comparing explicit and implicit functions through the equivalent equations y = x² + 1 and y − x² = 1
Review of explicit and implicit functions
Implicit functions slide asking which of five equations are difficult to express explicitly, with marked choices
Five equations introducing implicit differentiation
Worked example rewriting y² = 4x as y = ±2√x and differentiating both branches to obtain dy/dx = 2/y
Example 1: differentiation of explicit branches
Method slide listing four steps for implicit differentiation: differentiate, collect dy/dx terms, factor, and solve
Four-step implicit differentiation method
Worked example differentiating y² = 4x implicitly with the chain rule, giving 2y(dy/dx) = 4 and dy/dx = 2/y
Example 1 revisited using implicit differentiation
Worked example differentiating x² + y² = 4 implicitly, using the chain rule and solving for dy/dx = −x/y
Example 2: implicit differentiation of a circle
Worked example differentiating x² + y³ = 8 implicitly, using the chain rule to obtain dy/dx = −2x/(3y²)
Example 3: differentiating an equation with y³
Worked example using the product rule on x + x²y + y³ = 100, then collecting and factoring dy/dx terms
Example 4: applying the product rule to x²y
Worked example differentiating x³ + y³ − 9xy = 0 with the product rule, yielding dy/dx = (3y − x²)/(y² − 3x)
Example 5: product rule and derivative simplification
Attributes
Subject

Math, Calculus

Grades

Grade 12

Types

Teacher Tools, Lesson Plans

File

Microsoft PowerPoint

Editable
No
Author
Maths Support Centre
Rating
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About This Product

PowerPoint presentation, 15 slides explaining how to differentiate implicit functions

What's Included

PowerPoint presentation, 15 slides

Resource Tags

calculus diffrentiation implicit function

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