Sample Derivative Mastery Test
(Answers reflect no simplifying)
1. y = sin x
y' = cos x
2. y = cos x
y' = - sin x
3. y = tan x y' = sec2x
4. y = sec x
y' = sec x tan x
5. y = cot x y' = - csc2x
6. y = csc x
y' = -
csc x cot x
7. y = arcsin x
y' = 1/sqrt(1 - x2)
8. y = arctan x y' = 1/(1 + x2)
9. y = arcsec x y' = 1/(x sqrt(x2 - 1))
10. y = log7x
y' = 1/(x ln7)
11. y = ln
x
y' = 1/x
12. y = ex
y' = ex
13. y = ep
y' = 0
14. y = 7x
y' = 7x ln 7
15. y = x23
y' = 23x22
16. y =
1/x
y' = - x-2
17. y = x5 + 5x
y' = 5x4 + 5x ln
5
18. y =
sqrt(x) y' = (1/2)x^(-1/2)
19. y = x -3/4
y' = (-3/4)x^(-7/4)
20. xp +
y' = (p + 1)x^(p)
21. y = x sin(x) y' = 1*sin(x) + x*cos(x)
22. y = x/sin(x) y' = (1*sin(x) - x*cos(x))/(sin(x))2
23. y = tan(x)/ln(x) y' = (sec2x*ln x - tan x 81/x)/(ln(x))2
24. y = sqrt(tan(x)) y' = (1/2)(tan(x))^(-1/2)*sec2x
25. y = esin(x) y' = esin(x)cos(x)
26. y = ln(sin(x)) y' = 1/(sin(x)) *cos(x)
27. y = sin(ln(x)) y' = cos(ln(x))*1/x
28. y = xsin(x) ln y = ln(xsin(x))32. y = (tan x)5
y' = 5(tan x)4(sec2x)
33. y = tan x5 y' = sec2(x5) (5x4)
34. y = arctan(tan(3)) y' = 0
35. y = arctan(cos(x)) y' = 1/(1 + (cos(x))2)(-sin(x))
36. y = e(sin(x))^3
y' = e(sin(x))^3(3sin2(x) cos(x))
37. y = x ex sin(x) y' = 1*ex*sin(x) + x*ex*sin(x) + x*ex*cos(x)
38. y = x ex/sin(x) y' = ((1*ex + x*ex)sin x - (x*ex)(cos x))/sin2x
39. y4 + xy = x2
Solve for
y’ 4y3y' + 1*y + x*1*y' = 2x
y'(4y3 + x*1) = 2x
- y
y' = (2x - y)/(4y3 + x·*1)
40. y = x2/f(x) Find y’ in terms
of f and f ‘.
y' = (2x*f(x) - x2*f
'(x))/(f(x))2