Millersville University Name
Department of Mathematics
MATH 161 Calculus I , Quiz 10
December 3, 2004
Please answer the following questions. Your answers will be evaluated on their correctness,
completeness, and use of mathematical concepts we have covered. Please show all work and
write out your work neatly. Answers without supporting work will receive no credit.
1. Find the following derivative using properties of the natural logarithm as needed.
d
dx
ln sx3
x5+ 1
d
dx
ln sx3
x5+ 1
=d
dx "1
2ln x3
x5+ 1#
=1
2
d
dx "ln x3
x5+ 1#
=1
2
d
dx hln x3−ln(x5+ 1)i
=1
2
d
dx h3 ln x−ln(x5+ 1)i
=3
2
d
dx [ln x]−1
2
d
dx hln(x5+ 1)i
=3
2
1
x−1
2
1
x5+ 1
d
dx hx5+ 1i
=3
2x−1
2
1
x5+ 1 h5x4i
=3
2x−5x4
2(x5+ 1)
