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AP Calculus AB/BC. 3.7 Implicit Differentiation, p. 157 Day 1. Example. 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. 1 Differentiate both sides w.r.t. x. 2 Solve for . See p. 159.

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## 3.7 Implicit Differentiation, p. 157 Day 1

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**AP Calculus AB/BC**3.7 Implicit Differentiation, p. 157 Day 1**Example**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.**1 Differentiate both sides w.r.t. x.**2 Solve for . See p. 159 Example This can’t be solved for y. Using the Product Rule This technique is called implicit differentiation.**Example**Distribute the sec2 and subtract 1.**We need the slope. Since we can’t solve for y, we use**implicit differentiation to solve for . Example Find the equations of the lines tangent and normal to the curve at . Note product rule.**Find the equations of the lines tangent and normal to the**curve at . tangent: normal: p Day 1**AP Calculus AB/BC**3.7 Implicit Differentiation, p. 157 Day 2**Find if .**Substitute back into the equation. Higher Order Derivatives p Day 2

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