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3.7

3.7. Implicit Differentiation. Quick Review. Quick Review. Quick Review. Quick Review Solutions. Quick Review Solutions. Quick Review Solutions. What you’ll learn about. Implicitly Defined Functions Lenses, Tangents, and Normal Lines Derivatives of Higher Order

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3.7

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  1. 3.7 Implicit Differentiation

  2. Quick Review

  3. Quick Review

  4. Quick Review

  5. Quick Review Solutions

  6. Quick Review Solutions

  7. Quick Review Solutions

  8. What you’ll learn about • Implicitly Defined Functions • Lenses, Tangents, and Normal Lines • Derivatives of Higher Order • Rational Powers of Differentiable Functions … and why Implicit differentiation allows us to find derivatives of functions that are not defined or written explicitly as a function of a single variable.

  9. Implicitly Defined Functions

  10. Implicitly Defined Functions

  11. Example Implicitly Defined Functions

  12. Implicit Differentiation Process

  13. Lenses, Tangents and Normal Lines In the law that describes how light changes direction as it enters a lens, the important angles are the angles the light makes with the line perpendicular to the surface of the lens at the point of entry (angles A and B in Figure 3.50). This line is called the normal to the surface at the point of entry. In a profile view of a lens, the normal is a line perpendicular to the tangent to the profile curve at the point of entry. Implicit differentiation is often used to find the tangents and normals of lenses described as quadratic curves.

  14. Lenses, Tangents and Normal Lines

  15. Example Lenses, Tangents and Normal Lines

  16. Example Lenses, Tangents and Normal Lines

  17. Example Derivatives of a Higher Order

  18. Rule 9 Power Rule For Rational Powers of x

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