Unit 3 Lesson 5: Implicit Differentiation

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Unit 3 Lesson 5: Implicit Differentiation AP Calculus Mrs. Mongold

Implicit Differentiation Use this when we have an equation we want to differentiate that cannot be solved for y. Differentiate using all rules to date with respect to x and whenever differentiating something with a y we have to put dy/dx behind it.

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 .

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.

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

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

Homework Packet Lesson 2.5/ 2-40 Even