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3.7 Implicit Differentiation, p. 157 Day 1 - PowerPoint PPT Presentation


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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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    1. AP Calculus AB/BC 3.7 Implicit Differentiation, p. 157 Day 1

    2. 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.

    3. 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.

    4. Example Distribute the sec2 and subtract 1.

    5. 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.

    6. Find the equations of the lines tangent and normal to the curve at . tangent: normal: p Day 1

    7. AP Calculus AB/BC 3.7 Implicit Differentiation, p. 157 Day 2

    8. Find if . Substitute back into the equation. Higher Order Derivatives p Day 2