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Calculus I                                                          Quiz #7                            October 28, 2004

Name____________________                   R.  Hammack                              Score ______
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(1) Find derivatives of the following functions.
  
(a)  f(x) = cot(x) + x^3sec(x)

       f ' (x) = -csc^2(x) + 3x^2sec(x) + x^3sec(x) tan(x)



(b)   f(x) = cos(x) sin(x^3)

        f ' (x) = -sin(x) sin(x^3) + cos(x) cos(x^3) 3x^2


(c)  f(x) = (x^3 + 8)^(1/2)

      f(x) = (x^3 + 8)^(1/2)  f ' (x) = 1/2 (x^3 + 8)^(-1/2) 3x^2 = (3x^2)/(2 (x^3 + 8)^(1/2))



(2)  Suppose functions f and g and their derivatives obey the following table. x f(x) f ' (x) g(x) g ' (x) 0 0 1 ... 2 1 2 2 -2 3 2 1 -2 -1 5
If    h(x) = 3f(x) + f(g(x)),    find h ' (0).

h ' (x) = 3f ' (x) + f ' (g(x)) g ' (x)  h ' (0) = 3f ' (0) + f ' (g(0)) g ' (0) = 3 · 1 + f ' (2) · 2 = 3 + (-2) (2) = -1