1 / 4

Math 1304 Calculus I

Math 1304 Calculus I. 3.9 – Related Rates. For your reference: A good working set of rules. Constants: If F(x) = c, then f’(x) = 0 Powers: If F(x) = f(x) n , then F’(x) = n f(x) n-1 f’(x) Exponentials: If F(x) = a f(x) , then F’(x) = (ln a) a f(x) f’(x)

gpenney
Download Presentation

Math 1304 Calculus I

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. Math 1304 Calculus I 3.9 – Related Rates

  2. For your reference: A good working set of rules • Constants: If F(x) = c, then f’(x) = 0 • Powers: If F(x) = f(x)n, then F’(x) = n f(x)n-1 f’(x) • Exponentials: If F(x) = af(x), then F’(x) = (ln a) af(x) f’(x) • All trigonometric functions: If F(x) = sin(f(x)), then F’(x) = cos(f(x)) f’(x) If F(x) = cos(f(x)), then F’(x) = - sin(f(x)) f’(x) • Hyperbolic functions • All inverse trig functions • Scalar mult: If F(x) = c f(x), then F’(x) = c f’(x) • Sum: If F(x) = g(x) + h(x), then F’(x) = g’(x) + h’(x) • Difference: If F(x) = g(x) - h(x), then F’(x) = g’(x) - h’(x) • Multiple sums: derivative of sum is sum of derivatives • Linear combinations: derivative of linear combo is linear combo of derivatives • Product: If F(x) = g(x) h(x), then F’(x) = g’(x) h(x) + g(x)h’(x) • Multiple products: If F(x) = g(x) h(x) k(x), then F’(x) = g’(x) h(x) k(x) + g(x) h’(x) k(x) + g(x) h(x) k’(x) • Quotient: If F(x) = g(x)/h(x), then F’(x) = (g’(x) h(x) - g(x)h’(x))/(h(x))2 • Composition: If F = fog is a composite, defined by F(x) = f(g(x)) then F'(x) = f'(g(x))g'(x)

  3. Steps for Solving Related Rate Problems • Read the problem carefully • Draw a diagram if appropriate and possible • Introduce notation. Assign variable names • Express the given information in terms of functions and their derivatives • Write down the formulas that express these relationships • Use the chain rule to help with implicit differentiation • Substitute and simplify where appropriate • Solve the resulting equations as you can • Verify that you answers are in the feasible range of values for the problem.

  4. Examples • Types of problems • Volumes of spheres, boxes, and cones • See formulas inside front cover • Examples 1, 3 • Ladders and roads • Use distance formula (Pythagorean formula) • Examples 2, 4 • Rotating things (Search lights, etc.) • Use trigonometry • Example 5

More Related