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