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Implicitly Defined Functions

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Learn how to find slopes using implicit differentiation for implicitly defined equations. Get equations for tangent and normal lines with higher-order derivatives examples.

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Implicitly Defined Functions

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Presentation Transcript

  1. Implicitly Defined Functions

  2. Explicitly Defined Function

  3. Implicitly Defined Equation

  4. Implicitly Defined Functions

  5. Implicit Differentiation Process

  6. Example Implicitly Defined Functions

  7. This is not a function, but it would still be nice to be able to find the slope. Do the same thing to both sides. Note use of chain rule.

  8. This can’t be solved for y.

  9. We need the slope. Since we can’t solve for y, we use implicit differentiation to solve for . Find the equations of the lines tangent and normal to the curve at . Note product rule.

  10. Find the equations of the lines tangent and normal to the curve at . tangent: normal:

  11. Example Derivatives of a Higher Order

  12. Find if . Higher Order Derivatives

  13. Examples

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