1 / 14

The Chain Rule

The Chain Rule. Section 3.6c. Suppose that functions f and g and their derivatives have the f ollowing values at x = 2 and x = 3. 2. 8. 2. 1/3. –3. 3. 3. –4. 5. Evaluate the derivatives with respect to x of the following c ombinations at the given value of x . (a).

oya
Download Presentation

The Chain Rule

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. The Chain Rule Section 3.6c

  2. Suppose that functions f and g and their derivatives have the following values at x = 2 and x = 3. 2 8 2 1/3 –3 3 3 –4 5 Evaluate the derivatives with respect to x of the following combinations at the given value of x. (a) at x = 2 At x = 2:

  3. Suppose that functions f and g and their derivatives have the following values at x = 2 and x = 3. 2 8 2 1/3 –3 3 3 –4 5 Evaluate the derivatives with respect to x of the following combinations at the given value of x. (b) at x = 3 At x = 3:

  4. Suppose that functions f and g and their derivatives have the following values at x = 2 and x = 3. 2 8 2 1/3 –3 3 3 –4 5 Evaluate the derivatives with respect to x of the following combinations at the given value of x. (c) at x = 3 At x = 3:

  5. Suppose that functions f and g and their derivatives have the following values at x = 2 and x = 3. 2 8 2 1/3 –3 3 3 –4 5 Evaluate the derivatives with respect to x of the following combinations at the given value of x. (d) at x = 2

  6. Suppose that functions f and g and their derivatives have the following values at x = 2 and x = 3. 2 8 2 1/3 –3 3 3 –4 5 Evaluate the derivatives with respect to x of the following combinations at the given value of x. (e) at x = 2

  7. Suppose that functions f and g and their derivatives have the following values at x = 2 and x = 3. 2 8 2 1/3 –3 3 3 –4 5 Evaluate the derivatives with respect to x of the following combinations at the given value of x. (f) at x = 2

  8. Suppose that functions f and g and their derivatives have the following values at x = 2 and x = 3. 2 8 2 1/3 –3 3 3 –4 5 Evaluate the derivatives with respect to x of the following combinations at the given value of x. (g) at x = 3

  9. Suppose that functions f and g and their derivatives have the following values at x = 2 and x = 3. 2 8 2 1/3 –3 3 3 –4 5 Evaluate the derivatives with respect to x of the following combinations at the given value of x. (h) at x = 2

  10. Suppose that functions f and g and their derivatives have the following values at x = 2 and x = 3. 2 8 2 1/3 –3 3 3 –4 5 Evaluate the derivatives with respect to x of the following combinations at the given value of x. (h) at x = 2

  11. Slopes of Parametrized Curves A parametrized curve (x(t), y(t)) is differentiable at t if x and y are differentiable at t. At a point on a differentiable parametrized curve where y is also a differentiable function of x, the derivatives dy/dt, dx/dt, and dy/dx are related by the Chain Rule: Usually, we write this in a different form… If all three derivatives exist and ,

  12. Practice Problems Find the equation of the line tangent to the curve at the point defined by the given value of t. Find the three derivatives:

  13. Practice Problems Find the equation of the line tangent to the curve at the point defined by the given value of t. The line passes through: And has slope: Equation of the tangent line:

  14. Practice Problems Find the equation of the line tangent to the curve at the point defined by the given value of t. Derivatives: Slope: Point: Equation of the tangent line:

More Related