14209an4.7-10

14209an4.7-10 - c Kendra Kilmer Section 4.4 The Chain Rule...

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Unformatted text preview: c Kendra Kilmer February 27, 2009 Section 4.4 - The Chain Rule Definition: A function m is a composite of functions f and g if The domain of m is the set of all numbers x such that x is in the domain of g and g(x) is in the domain of f . Example 1: Given f (u) = u2 + 5 and g(x) = ex , find the following compositions: a) f (g(x)) b) g( f (u)) c) f ( f (u)) d) g(g(x)) Example 2: Write each function as a composition of two simpler functions. a) h(x) = x3 + 1 b) k(x) = 25x+7 7 c Kendra Kilmer February 27, 2009 Chain Rule: If y = f (u) and u = g(x) define the composite function m(x) = f [g(x)] then General Derivative Rules: If y = [ f (x)]n then If y = ln[ f (x)] then If y = logb [ f (x)] then If y = e f (x) then if y = b f (x) then Example 3: Differentiate the following: a) f (x) = (4x2 + 7x)5 b) g(x) = 6(x1/2 - 3x)4 c) y = 5 (t 2 + 3t + 4)4 d) F(x) = ex 2 8 c Kendra Kilmer February 27, 2009 e) G(x) = 3x 4 -x f) H(x) = 3x5 ex 4 g) y = ln(1 + x2 ) ln[(x4 + 8x)2 ] h) y = 6 x + 3x2 - 1 i) h(x) = 4 3 (3x+2)5 j) s(t) = e2t+1 et-4 9 c Kendra Kilmer February 27, 2009 k) y = log7 x-1 x+2 l) y = 5 (ln(x2 + x)) 3 x m) f (x) = (4x2 + 5)6 ( 3 (3x4 - 5x + 7)4 ) Example 4: Find the value(s) of x where the tangent line is horizontal for f (x) = x2 (2 - 3x)3 Example 5: You are given the following information: g(4) = 8, g (4) = 3, f (4) = 7, f (8) = 6, f (3) = 5. If h(x) = f (g(x)), what is h (4)? Section 4.4 Homework Problems: 17,23,27,31-37(odd),41,47-57(odd),61,63,67,69,79,85,87,91,93 and supplemental problems 10 ...
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14209an4.7-10 - c Kendra Kilmer Section 4.4 The Chain Rule...

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