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

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Presentation transcript:

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

Notes about the chain rule

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

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

Example 3

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

Find if. Substitute back into the equation. Example 5