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Unit 3 Lesson 5: Implicit Differentiation

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

2 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.

3 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.

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

5 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.

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

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

8 Homework Packet Lesson 2.5/ 2-40 Even


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