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3.8 Implicit Differentiation Niagara Falls, NY & Canada Photo by Vickie Kelly, 2003.

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Presentation on theme: "3.8 Implicit Differentiation Niagara Falls, NY & Canada Photo by Vickie Kelly, 2003."— Presentation transcript:

1 3.8 Implicit Differentiation Niagara Falls, NY & Canada Photo by Vickie Kelly, 2003

2 Notes about the chain rule

3 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. Example 1

4 This can’t be solved for y. This technique is called implicit differentiation. 1 Differentiate both sides w.r.t. x. 2 Solve for. Example 2

5 Example 3

6 Find the point(s) at which the curve has horizontal or vertical tangent lines. Note product rule. Example 4

7 Find if. Substitute back into the equation. Example 5

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