Victor Camacho
Assignment Homework 1 due 08/30/2012 at 11:00pm MDT
1. (1 pt) Library/Rochester/setDerivatives7Log/sc3 7 2.pg
If f (x) = 5 ln(3 + x), find f 0 (x).
math1220fall2012-2
9. (1 pt) Library/Rochester/setDerivatives7Log/mec9.pg
Let
f (x) = ln[x5 (x + 4)7 (x2 + 9)6 ]
f 0 (x) =
Find f 0 (4).
10. (1 pt) Library/Rochester/setDerivatives7Log/osu dr 7 3.pg
dy
Find
for each of the following functions
dx
5x − 4
y = ln √
x 7 x2 + 1
2. (1 pt) Library/Rochester/setDerivatives7Log/mec8 mo.pg
Let
p
f (x) = ln
(6x + 6)(5x − 4)
f 0 (x) =
dy
=
dx
3. (1 pt) Library/Rochester/setDerivatives7Log/sc3 7 4.pg
If f (x) = 4 cos(4 ln(x)), find f 0 (x).
y = xcos(x)
dy
=
dx
Find f 0 (2).
11. (1 pt) Library/Rochester/setDerivatives7Log/mec3.pg
Let
f (x) = 5x2 ln x
4. (1 pt) Library/Rochester/setDerivatives7Log/sc3 7 32.pg
If f (x) = 10(sin(x))x , find f 0 (3).
f 0 (x) =
f 0 (e4 ) =
12. (1 pt) Library/Rochester/setDerivatives7Log/osu dr 7 1.pg
Let
5. (1 pt) Library/Rochester/setDerivatives7Log/mec8.pg
Let
r
4x + 5
f (x) = ln
5x − 9
0
f (x) =
y = xlog7 (x)
Then
dy
=
dx
Note: You must express your answer in terms of natural logs,
as Webwork doesn’t understand how to evaluate logarithms to
other bases.
6. (1 pt) Library/Rochester/setDerivatives7Log/mec5.pg
Let
f (x) = −4 log7 (x)
0
f (x) =
f 0 (1) =
13. (1 pt) Library/Rochester/setDerivatives7Log/mec7f.pg
Let
f (x) = x3x
7. (1 pt) Library/Rochester/setDerivatives7Log/mec12.pg
Let
f (x) = 8x log5 (x)
f 0 (x) =
Use logarithmic differentiation to determine the derivative.
f 0 (x) =
14. (1 pt) Library/Rochester/setDerivatives7Log/mec4.pg
Let
8. (1 pt) Library/Rochester/setDerivatives7Log/mec6.pg
Let
f (x) = ln(x6 )
f 0 (x) =
f 0 (e2 ) =
f (x) = [ln x]4
f 0 (x) =
f 0 (e2 ) =
1
21. (1 pt) Library/Rochester/setIntegrals14Substitution/sc5 5 38.pg
Evaluate the definite integral.
15. (1 pt) Library/UVA-Stew5e/setUVA-Stew5e-C03S08-DerivLogs/38-44a.pg
Let
Z π/1
f (x) = 5x log2 (x)
f 0 (x) =
esin(x) cos(x)dx
0
Hint: In WeBWorK, you must use
ln(x)
for logb (x).
ln(b)
16. (1 pt) Library/UCSB/Stewart5 3 8/Stewart5 3 8 41.pg
22. (1 pt) Library/Rochester/setIntegrals14Substitution/sc5 5 24.pg
Evaluate the indefinite integral.
Use logarithmic differentiation to find the derivative of the
function.
y = xsin x
y0 =
Z
x1
dx
x2 + 7
17. (1 pt) Library/UCSB/Stewart5 3 8/Stewart5 3 8 42.pg
[NOTE: Remeber to enter all necessary *, (, and ) !!
Enter arctan(x) for tan−1 x , sin(x) for sin x . ]
Use logarithmic differentiation to find the derivative of the
function.
y = (sin x)x
y0 =
23.
(1
pt)
Library/Rochester/setIntegrals14Substitution-
/S05.05.Substitution.PTP12.pg
Evaluate the indefinite integral.
18. (1 pt) Library/WHFreeman/Rogawski Calculus Early Transcendentals Second EditionZ
/3 Differentiation/3.9 Derivatives of General Exponential and Logarithmic Functionsx+1
dx
/3.9.45.pg
x2 + 2x + 2
From Rogawski ET 2e section 3.9, exercise 45.
Find the derivative using the methods of Example 6 in the
+C
text.
y = x6x
y0 =
24. (1 pt) Library/Rochester/setIntegrals14Substitution/sc5 5 7.pg
Evaluate the indefinite integral.
19. (1 pt) Library/Rochester/setIntegrals14Substitution/sc5 5 49.pg
Evaluate the definite integral.
Z 1
0
Z
dx
1x + 5
(ln(x))8
dx
x
+C
25. (1 pt) Library/UVA-Stew5e/setUVA-Stew5e-C05S05-Substitution/5-5-32.pg
Evaluate the indefinite integral.
20. (1 pt) Library/Rochester/setIntegrals14Substitution/sc5 5 8.pg
Evaluate the indefinite integral.
Z
Answer =
Z
ex
dx
ex + 7
3
x2 ex dx
Integral =
[NOTE: Remember to enter all necessary *, (, and ) !!
Enter arctan(x) for tan−1 x , sin(x) for sin x . ]
+C
c
Generated by WeBWorK,
http://webwork.maa.org, Mathematical Association of America
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