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Implicit Differentiation

Implicit Differentiation. Explicit vs. Implicit. The function is “implied” by an equation. You can’t separate the variables. The function can be expressed as an equation in terms of one variable. Difficult to express y in terms of x. variables agree, use Power Rule.

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Implicit Differentiation

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  1. Implicit Differentiation Explicit vs. Implicit The function is “implied” by an equation. You can’t separate the variables. The function can be expressed as an equation in terms of one variable Difficult to express y in terms of x

  2. variables agree, use Power Rule variables don’t agree, must use Chain Rule For Example:

  3. Let’s look closer at this: Chain Rule: Need to rename some things Let Then The Chain Rule becomes:

  4. So, every term with a ‘y’ in it will include the dy/dx term. Differentiate with respect to x Power Rule Power Rule Chain Rule

  5. Now solve for dy/dx Move all terms with dy/dx to one side, then factor. Now isolate dy/dx Notice the derivative contains both x and y

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