3.7 Implicit Differentiation, p. 157 Day 1

1 / 8

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

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## 3.7 Implicit Differentiation, p. 157 Day 1

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
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