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I will be collecting your homework tomorrow

Hi. I will be collecting your homework tomorrow. Chain Rule How to differentiate a composition. Y is a function of u, and u is a function of x. Basic Idea:. Compositions. Let Write each as a composition of 2 or more functions. More Composition review. Given the functions, find.

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I will be collecting your homework tomorrow

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  1. Hi I will be collecting your homework tomorrow

  2. Chain RuleHow to differentiate a composition.Y is a function of u, and u is a function of x Basic Idea:

  3. Compositions • Let • Write each as a composition of 2 or more functions

  4. More Composition review • Given the functions, find

  5. Let’s talk with math dude… So how do we differentiate a composition? The idea is stuck to my head

  6. Let y = 14x-8 • Let’s write y = 2(7x-4). • See a composition? • Y = 2u and u = 7x-4 • Find • dy/du= du/dx = dy/dx= (2)(7)=14 dy/du • du/dx = dy/dx

  7. Math dude’s gear idea was pretty intuitive …do you know why? • If y is a function of u, and u is a function of x then, • www.mathizaverb.com see chain rule link under calculus corkboard.

  8. Chain Rule Again • If f is differentiable at u, which is really g(x) and g is differentiable at x, then f◦g(x) is differentiable at x and…. function notation

  9. Examples and Problems Differentiate each.

  10. Problems to Deepen Understanding  1. Assume that h(x) = f( g(x) ) , where both f and g are differentiable functions. If g(-1)=2, g'(-1)=3, and f '(2)=-4 , what is the value of h'(-1) ? 2.  Assume that , h(x)= (f(x))3 where f is a differentiable function. If  f(0) = -1/2 and f ‘ (0) = 8/3  , determine an equation of the line tangent to the graph of h at x=0.

  11. Solutions Solution to problem 1 Solution to problem 2

  12. Physics • A particle moves along a straight line with displacement s(t) , velocity v(t) and accel a(t). Show • Hint: Write accel, veloc. in terms of differentials, then apply chain rule. • What is the meaning of dv/dt and dv/ds?

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