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Calculus I                                             Quiz #10                          April 27, 2004

Name____________________       R.  Hammack                          Score ____
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(1) Simplify the following expressions as much as possible.

(a)  e^ln(5) =5

(b) ln ( 2 - e^0) = ln ( 2 - 1) = ln ( 1) = 0

(c)  ln ( e^(1/2)) =1/2

(d)  ln ( e) =1


(2) Find the derivatives.

(a)  d/dx[3^x] =ln(3) 3^x

(b) d/dx[e^x] = e^x

(c)  d/dx[log_3(x)] = 1/(x ln(3))

(d)  d/dx[ ln(x) ] =1/x



(3) Find the derivatives.

(a)  d/dx[e^(x tan(x))] = e^(x tan(x))(tan(x) + x sec^2(x))


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


(c)  d/dx[ln(x^3 - 45x)] = (3x^2 - 45)/(x^3 - 45x)