Calculus I Test 2. February 21, 2003 NAME:_____________________________________________
PART I. Find the derivative y0=dy
dx of each of the following functions. Do
basic simpli…cations only (simple additions, multiplications, and combining like
terms). Parentheses must be correctly placed.
1. y=x45x3+x27x+ 8
2. y=3
px
3. y=x2
1+x3
4. y=5+3x+x28
5. y=x3sin(x)
6. y= ln
2+5x+x2
7. y= sin(tan(x))
8. y= cos(10x+p3)
9. y= sin1(5x)
10. y=xe3x
11. y=xp1 + x2
12. y= log3(x)
PART II. Do as instructed.
13.Find the equation of the line tangent to the graph of y=e5x
1+e5xat the
point (x; y) = (0;1
2):Simplify your answer.
14. Let g(x) = tan1(x). Find g00 (3):
15. Use implicit di¤erentiation to …nd y0=dy
dx if xand ysatisfy x3+ 2xy +
y3= 4:
1