3.6 Warm-Up Find y´´ Find the Derivative:

3.6a Implicit Differentiation State Standard – 6.0 Students use implicit differentiation in a wide variety of problems. Objective – To be able to use implicit differentiation

Implicit Differentiation (Takes Four Steps) 1) Differentiate both sides of the equation with respect to ‘x’, treating ‘y’ as a differentiable function of ‘x’. 2) Collect the terms with the dy/dx on one side of the equation. 3) Factor out the dy/dx. 4) Solve for dy/dx.

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.

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

Explicit- Implicit- From www.Dictionary.com 6.Mathematics. (of a function) having the dependent variable expressed directly in terms of the independent variables, as y = 3x + 4. Implicit- 4.Mathematics. (of a function) having the dependent variable not explicitly expressed in terms of the independent variables, as x2 + y2 = 1.

Example 1 Find of

Example 2 Find of

Example 3 Find of

Example 4 Find of

3.6a Assignment Pg. 233 1a, 2a, 3a, 5 – 9, 11, 13, 14, and 20