October 18, 1999
Math 111 E and H — Exam II
Show all work clearly for partial credit. Do not use the graphing capabilities of your calculator.
1. (36 points) Find dy/dx:
(a) y=xsin x(b) y=x+ 5
x2+ 1 (c) y= tan23x
(d) y=x2
−2x(e) x3y−2ey= 5 (in terms of xand y) (f) y= (x2+ 2)x
2. (15 points) (a) If y=√ln x, what is y0?
(b) Find the equation of the tangent line to y= ln xat x=e4.
3. (15 points) The distance units on a number line are centimeters (cm). The position of a point
on the line at time tsec is given by s(t) = t4
−24t2+ 8t+ 5. At what (positive) time(s) is
(are) the acceleration of the point equal to 0, and what are the position and velocity at this
time (these times)? Include units.
4. (10 points) If the edge of a cube is growing at 4 inches/min, how quickly is the total surface
of the cube increasing when the edge is 20 inches long?
5. (10 points) Two of these functions A,B,C,D are the first and second derivatives of another of
these, and the remaining function is unrelated to the others. Which of these is f, which is
f0, which is f”, and which is the unrelated g, and why?
6. (9 points) Use the derivative rules for sin xand cos xto derive the derivative rule for cot x.
