1. 3.7 Implicit Differentiation

2. 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.

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

4. Find the equations of the lines tangent and normal to the curve at .
We need the slope. Since we can’t solve for y, we use implicit differentiation to solve for
Note product rule.

5. Find the equations of the lines tangent and normal to the curve at .

6. Higher Order Derivatives
Find if
Substitute
back into the equation.

7. Implicit Differentiation Process Summarized
Differentiate both sides of the equation with respect to x.
Collect like terms with dy/dx on one side of the equation.
Factor out dy/dx.
Solve for dy/dx.

8. No homework tonight!

9. Sucker! What are you crazy? Of course there is homework…lol, lol, rofl.
C3.7 #3-45 (multiples of 3), 40-42, 46, 48, 50
Research: What was the intent of Descartes when he created the folium?