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)nn!/(1+x)n+1
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2. If f(x) = (x e3x)/(1 + x) for x   1, then f(1) = ?

 A. 3e3/4 B. 5e3/4 C. 7e3/4 D. 9e3/4 E. 4e3
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3. If u = (x2+9)1/2 and v = 3x2-2x, then what is du/dv as a function of x?

 A. 1/(4(3x-1)(x2+9)1/2) for x   1/3 B. (3x-1)/(2(x2+9)1/2) C. (2x(3x-1))/(x2+9)1/2 D. x/(2(3x-1)(x2+9)1/2) for x   1/3
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4. The volume (in gallons) of water in a tank after t hours is given by f(t) = 600 sin2(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)cos2(Pi*t/12) E.600cos2(Pi*t/12)
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5. What is the slope of the line tangent to the curve y3 - x2y + 6 = 0 at the point (1,-2)?

 A. -(2/5) B. -(4/11) C. 4/11 D. 11/4 E. 8
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6. If f(x) = xex/sin(x) for 0 < x <
p , then f(x) =

 A. ex/cosx B. ex(x+1)/cosx C.ex[sinx+xcosx/sin2x] D.ex[x(sinx+cosx)+sinx]/sin2x E.ex[x(sinx-cosx)+sinx]/sin2x
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7. What is the slope of the tangent line to the curve x3 + y3 - 3xy = 13 at the point (2,-1)?

 A. -5 B. -4 C. -1/5 D. 4 E. 5
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8. Let f(x) = x2 ln x - (x3 + 3)/2x for x > 0. Then f(x) =

 A. 2 - (3x2/2) B. 2x ln x + x - (3x2/2) C. 2x ln x + (3/2x2) D. 2x ln x + 2x - (3/2x2) E. 2 - x + (3/2x2)
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9. Let f(x) = 2sin x. Then f"(0) =

 A. -ln 2 B. -(ln 2)2 C. 0 D. (ln 2)2 E. ln 2
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10. Let f(x) = sin(2x + 1) and g(x) = x3 + 3 for all real x. Which of the following is equal to the derivative of the composite function f[g(x)]?

 A. sin(2x3 + 7) B. cos(2x3 + 7) C. 6 sin(2x3 + 7) D. 6 cos(2x3 + 7) E. 6x2 cos(2x3 + 7)
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11. The equation y2 exy = 9 e-3 x2 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
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12. A point moves along a number line so that its position at time t >= 0 is s(t) = 2t3 - 15t2 + 36t - 10. What is the position of the point when it first changes direction?

 A. -63 B. 0 C. 17 D. 18 E. 98
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13. What is the derivative of f(x) = sin(xx) for x > 0?

 A. xx(1 + ln x) cos(xx) B. xx cos(xx) C. xx ln x cos(xx) D. cos(xx) E. cos(xx ln x)
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14. What is the derivative of f(x) = 4x(x2 + 1)3 ?

 A.4(x2 + 1)2(x2 + 3x + 1) B. 4(x2 + 1)2(7x2 + 1) C. 8x2(x2 + 1)3 D. 12x(x2 + 1)2 E. 24x2(x2 + 1)2
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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. x1/3
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16. What is the slope of the line tangent to the circle x2 + y2 = 45 at the point (6,-3)?

 A. -6 B. -1/2 C. 1/6 D. 2 E. 11/2
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