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Lesson 2.5 Implicit Differentiation

Lesson 2.5 Implicit Differentiation. Implicit & Explicit Forms Implicit Form Explicit Form Derivative Explicit: y in terms of x Implicit: y and x together Differentiating: want to be able to use either. Differentiating with respect to x Derivative →

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Lesson 2.5 Implicit Differentiation

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  1. Lesson 2.5Implicit Differentiation

  2. Implicit & Explicit Forms Implicit Form Explicit Form Derivative Explicit: y in terms of x Implicit: y and x together Differentiating: want to be able to use either

  3. Differentiating with respect to x Derivative → Deriving when denominator agrees → use properties Deriving when denominator disagrees → use chain rule & properties Denominator agrees - properties Denominator disagrees – chain rule

  4. Derive implicitly:

  5. Implicit Differentiation Trying to find

  6. Function: Table of values (3): Differentiate: ImplicitlyExplicitly Check values:

  7. Example: Find the derivative

  8. Example: Determine the slope at the point (1,1) Problem Set 2.5

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