1. Let f(x) = 1/(1+x) for x 1. What is the nth derivative, f^{(n)}(x)?
A. n!(1+x)^{n+1} 
B. n!/(1+x)^{n+1} 
C. n!/(1+x)^{n+1} 
D. n!/(1+x)^{n} 
E. (1)^{n}n!/(1+x)^{n+1} 
2. If f(x) = (x e^{3x})/(1 + x) for x 1, then f(1) = ?
A. 3e^{3}/4 
B. 5e^{3}/4 
C. 7e^{3}/4 
D. 9e^{3}/4 
E. 4e^{3} 
3. If u = (x^{2}+9)^{1/2} and v = 3x^{2}2x, then what is du/dv as a function of x?
A. 1/(4(3x1)(x^{2}+9)^{1/2}) for x 1/3 
B. (3x1)/(2(x^{2}+9)^{1/2}) 
C. (2x(3x1))/(x^{2}+9)^{1/2} 
D. x/(2(3x1)(x^{2}+9)^{1/2}) for x 1/3 
4. The volume (in gallons) of water in a tank after t hours is given by f(t) = 600 sin^{2}(Pi*t/12) for 0 ú t ú 6. What is the rate of flow of water into the tank, in gallons per hour?
A.100(Pi)sin(Pi*t/12) 
B.100(Pi)cos(Pi*t/12)sin(Pi*t/12) 
C.1200cos(Pi*t/12)sin(Pi*t/12) 
D.50(Pi)cos^{2}(Pi*t/12) 
E.600cos^{2}(Pi*t/12) 
5. What is the slope of the line tangent to the curve
y^{3}  x^{2}y + 6 = 0 at the point (1,2)?
A. (2/5) 
B. (4/11) 
C. 4/11 
D. 11/4 
E. 8 
6. If f(x) = xe^{x}/sin(x) for 0 < x <
p ,
then f(x) =
A. e^{x}/cosx 
B. e^{x}(x+1)/cosx 
C.e^{x}[sinx+xcosx/sin^{2}x] 
D.e^{x}[x(sinx+cosx)+sinx]/sin^{2}x 
E.e^{x}[x(sinxcosx)+sinx]/sin^{2}x 

7. What is the slope of the tangent line to the curve x^{3} + y^{3}  3xy = 13 at the point (2,1)?
A. 5 
B. 4 
C. 1/5 
D. 4 
E. 5 
8. Let f(x) = x^{2} ln x  (x^{3} + 3)/2x for x > 0. Then f(x) =
A. 2  (3x^{2}/2) 
B. 2x ln x + x  (3x^{2}/2) 
C. 2x ln x + (3/2x^{2}) 
D. 2x ln x + 2x  (3/2x^{2}) 
E. 2  x + (3/2x^{2}) 
9. Let f(x) = 2^{sin x}. Then f"(0) =
A. ln 2 
B. (ln 2)^{2} 
C. 0 
D. (ln 2)^{2} 
E. ln 2 
10. Let f(x) = sin(2x + 1) and g(x) = x^{3} + 3 for all real x. Which of the following is equal to the derivative of the composite function f[g(x)]?
A. sin(2x^{3} + 7) 
B. cos(2x^{3} + 7) 
C. 6 sin(2x^{3} + 7) 
D. 6 cos(2x^{3} + 7) 
E. 6x^{2 }cos(2x^{3} + 7) 
11. The equation y^{2 }e^{xy} = 9 e^{3} x^{2} defines y as a differentiable function of x. What is the value of dy/dx for x = 1, y =3?
A. 15/2 
B. 9/2 
C. 3/2 
D. 6 
E. 15 
12. A point moves along a number line so that its position at time t >= 0 is s(t) = 2t^{3}  15t^{2} + 36t  10. What is the position of the point when it first changes direction?
A. 63 
B. 0 
C. 17 
D. 18 
E. 98 
13. What is the derivative of f(x) = sin(x^{x}) for x > 0?
A. x^{x}(1 + ln x) cos(x^{x}) 
B. x^{x} cos(x^{x}) 
C. x^{x }ln x cos(x^{x}) 
D. cos(x^{x}) 
E. cos(x^{x} ln x) 
14. What is the derivative of f(x) = 4x(x^{2} + 1)^{3} ?
A.4(x^{2} + 1)^{2}(x^{2} + 3x + 1) 
B. 4(x^{2} + 1)^{2}(7x^{2} + 1) 
C. 8x^{2}(x^{2} + 1)^{3} 
D. 12x(x^{2} + 1)^{2} 
E. 24x^{2}(x^{2} + 1)^{2} 
15. Which of the following functions is continuous everywhere, but has at least one point where it is not differentiable?
A. tan x 
B. x/x 
C. sin x 
D. e^{x} 
E. x^{1/3} 
16. What is the slope of the line tangent to the circle x^{2} + y^{2} = 45 at the point (6,3)?
A. 6 
B. 1/2 
C. 1/6 
D. 2 
E. 11/2 