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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