1 / 6

Chapter 2: Differentiation

Chapter 2: Differentiation. L2.5 Implicit Differentiation. Day 1 Warm up. Find dy/dx : a) b) 5x 2 – 3y = x + 10 for both a) and b) since they are the same equation!

italia
Download Presentation

Chapter 2: Differentiation

An Image/Link below is provided (as is) to download presentation 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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 2: Differentiation L2.5 Implicit Differentiation

  2. Day 1 Warm up Find dy/dx: a) b) 5x2 – 3y = x + 10 for both a) and b) since they are the same equation! When we have y on left and x’s on right, we find dy/dx using explicit differentiation.

  3. Implicit Differentiation When we can’t write y = ‘some fcn of x’, we use implicit differentiation, with the Chain Rule. Implicit Differentiation: • Differentiate both sides with respect to x. If term has a y in it, take derivative of y and multiply by dy/dx (from Chain Rule). • Collect terms with dy/dx on one side and factor out dy/dx. • Solve to get dy/dx = ….

  4. Implicit Differentiation Find . • y3 + y2 – 5y – x2 = −4 • From today’s warm up, we saw that dy/dx was the same for and 5x2 – 3y = x + 10 because they are the same equation. Find dy/dxusing implicit differentiation on the 2nd equation. Do you get the same result?? 3. x2y + xy2 = 6 4. See handout for other examples

  5. Warm up Find the slope of the tangent line at the point (3,4) on the semicircle: A circle is the union of two differentiable functions. x2 + y2 = 25 → There are two ways to get the slope of a tangent: • Break into separate functions and find explicit derivative of each. • Use implicit differentiation – get derivative of whole thing at once. Exercises: Find slope of tangent line for • x2 + 4y2 = 4 at 2. y4 = y2 – x2 at

  6. Implicit Differentiation Given sin y = x. Find dy/dx. Can you write dy/dx in terms of just x? Often the form of the derivative can be simplified by using the original equation or a prior derivative. Find if 2x3 − 3y2 = 8.

More Related