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Implicit Differentiation

Implicit Differentiation. Objective: To find derivatives of functions that we cannot solve for y. Implicit Differentiation. It is not necessary to solve an equation for y in terms of x in order to differentiate the function defined implicitly by the equation (but often it is easier to do so).

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Implicit Differentiation

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1. Implicit Differentiation Objective: To find derivatives of functions that we cannot solve for y.

2. Implicit Differentiation • It is not necessary to solve an equation for y in terms of x in order to differentiate the function defined implicitly by the equation (but often it is easier to do so). • Find dy/dx for . Can we solve this for y?

3. Implicit Differentiation • It is not necessary to solve an equation for y in terms of x in order to differentiate the function defined implicitly by the equation. • For example, we can take the derivative of with the quotient rule:

4. Implicit Differentiation • We can also take the derivative of the given function without solving for y by using a technique called implicit differentiation. We will use all of our previous rules and state the independent variable.

5. Example 2 • Use implicit differentiation to find dy/dx if

6. Example 2 • Use implicit differentiation to find dy/dx if

7. Example 2 • Use implicit differentiation to find dy/dx if

8. Example 2 • Use implicit differentiation to find dy/dx if

9. Example 3 • Use implicit differentiation to find if

10. Example 3 • Use implicit differentiation to find if

11. Example 3 • Use implicit differentiation to find if

12. Example 3 • Use implicit differentiation to find if

13. Example 3 • Use implicit differentiation to find if

14. Example 3 • Use implicit differentiation to find if

15. Example 3 • Use implicit differentiation to find if

16. Example 4 • Find the slopes of the tangent lines to the curve at the points (2, -1) and (2, 1).

17. Example 4 • Find the slopes of the tangent lines to the curve at the points (2, -1) and (2, 1). • We know that the slope of the tangent line means the value of the derivative at the given points.

18. Example 4 • Find the slopes of the tangent lines to the curve at the points (2, -1) and (2, 1). • We know that the slope of the tangent line means the value of the derivative at the given points.

19. Example 4 • Find the slopes of the tangent lines to the curve at the points (2, -1) and (2, 1). • We know that the slope of the tangent line means the value of the derivative at the given points.

20. Example 5 Use implicit differentiation to find dy/dx for the equation .

21. Homework • Page 241-242 • 1-23 odd • 27 (just use implicit)

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