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Calculus I                                                          Quiz #9                            November 17, 2004

Name____________________                   R.  Hammack                              Score ______
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(1)  The following cartoon appeared on September 16, 2004.

  Fox Trot •  bill amend


(a) How many pounds is the burger?  (1/256)^(1/4) = 1/256^(1/4) = 1^(1/4)/256^(1/4) = 1/4pound

 (b) How much does Today's Special cost?   FormBox[RowBox[{RowBox[{ln, (, RowBox[{e, ^, 3.99}], )}], =}], TraditionalForm]$3.99




(2)  Find the following derivatives.

  
(a)   d/dx[ 4^cos(x) ] = ln(4) 4^cos(x) (-sin(x)) = -sin(x) ln(4) 4^cos(x)


 (b)  d/dx[ ln(tan(x))] = sec^2(x)/tan(x) = 1/cos^2(x) cos(x)/sin(x) = 1/(cos(x) sin(x))



(c)  d/dx[ x^4e^(3x) ] = 4x^3e^(3x) + x^4e^(3x)(3) = 4x^3e^(3x) + 3x^4e^(3x)



 (d)  d/dx[ln(x)^(1/2)] = d/dx[(ln(x))^(1/2)] = 1/2 (ln(x))^(-1/2) 1/x = 1/(2xln(x)^(1/2))



 (e)  d/dx[ log_3(x)] =1/(ln(3) x)