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Unformatted text preview: 9/13/2010 1 Chain Rule, Plane Curves, and Parametric Equations Calculus I Section 3.5 2 The Chain Rule (Section 3.5) If y=f (u) is a differentiable function of u and u=g(x) is a differentiable function of x , then y=f (g(x)) is a differentiable function of x and or equivalently, In words: The derivative of the outside evaluated at the inside times the derivative of the inside. dx du du dy dx dy ⋅ = [ ] ) ( )) ( ( )) ( ( x g x g f x g f dx d ′ ⋅ ′ = Definition of a Plane Curve If f and g are continuous functions of t on an interval I, then the equations x = f(t) and y=g(t) are called parametric equations and t is called the parameter . The set of points (x,y) obtained as t varies over the interval I is called the graph of the parametric equations. Taken together, the parametric equations and the graph are called a plane curve , denoted by C . Example Compare n x = t 2 + 1, y=2t 2 – 1 n x = 1 – t 2 , y = 1 – 2t 2 Eliminating the Parameter Another way to find out information about...
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This note was uploaded on 01/12/2012 for the course MATH 2554 taught by Professor Pamelasatterfield during the Spring '11 term at NorthWest Arkansas Community College.
 Spring '11
 PamelaSatterfield
 Equations, Chain Rule, The Chain Rule, Parametric Equations

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