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:

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Presentation transcript:

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

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

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

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, see chain rule link under calculus corkboard.

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

Examples and Problems Differentiate each.

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. Problems to Deepen Understanding

Solutions Solution to problem 1 Solution to problem 2

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?