1. No category

Math 1432
Section 15247 MWF 10am – 11 am SEC 100
Dr. Melahat Almus
[email protected]
http://www.math.uh.edu/~almus
Office Hours in 222 Garrison (CASA):
Starting this week
Friday: 11:00 am – 2:00 p.m.
COURSE WEBSITE:
http://www.math.uh.edu/~almus/1432_fall14.htm
Visit my website regularly for announcements and course material!
If you e-mail me, please mention your course (1432) in the subject line.
1
Buy your popper (bubbling) forms and Course Access Code from the
Bookstore by this Friday. Know your class and section number to get the
correct bubbling forms.
Print off notes (4 per page unless you write large) before class to make
note-taking easier.
Reminder: Practice Test 1 and Test 1 close Wednesday 9/3.
They are BOTH REQUIRED.
2
Section 7.3/7.4 Quick Review. . .
ln x 
d
1
ln  x   ,
dx
x
x
1
1
dt x  0
t
for x  0
g'  x 
d
ln g  x  
dx
g x 
,
where g a positive function of x
dx
x0
 x  ln x  C ,
g'  x 
 g  x  dx  ln g  x   C , g  x   0



1
du  ln u  C ,
u
u0
3
4
f
f
1
x  e
x
f  x   ln x
f

1
f
1
 x   x
 f  x   x
   x
f e
f
x
1
 ln e
x
ln x
ln
x

e
x
 
5
x
d x
e e
dx
If u is a function of x, then
And,
x
x
u
u
d u
u du
e e
dx
dx
 e dx  e  C
 e du  e  C
6
Examples:
d 5x
e 
dx
e
7x
e
ln x

dx
dx =

sin e  2 x
e
2x

dx
7
Example: What is the domain of this function?
f  x   ln  ln  2x  
f ' x 
Example: Find y ’ for:
y  x 2 e 2 x  e x ln x
8
Example: Find y ’ for:
x
y  ln e  4x
9
1 x
Example: Find the equation of the tangent line to y  e
(1, 1).
Example: Find the slope of the normal line to y  ln e
(–2, 4).
x
at the point
2
at the point
10
Example:
e
1
x
 x 2 dx
11
Example:

4 x2  5x  4
x2 1
dx
12
Example: Use logarithmic differentiation to find the derivative of:
x2 x  1
y
2x  1
13
Example: Differentiate y = (cosx)(3x-2)
14
Exercise: Find the derivatives using logarithmic differentiation:
y  5x 
x 1
y  xcos x
Exercise:
2 x 1

f  x  x
, f ' 1  ?
15
Section 7.5
Arbitrary Powers; Other Bases
16
Find the derivative of an exponential function with base a (a number).
x
ya
u
ya
17
Find the derivative of a log function with base a.
lnx
lo g a x 
Use change of base formula:
lna
y  log a x
y  log a u
18
Example: Find the derivative of each.
y 2
x
3x
y 5
2

2
y  log 4 x  2

19
y  log  cos x 
y  log5  tan x 
20
1 x
 a dx  ln a a  c
x
1 u
 a du  ln a a  c
u
Examples:
x
 6 dx 
21
x
dx 
5x
dx 
4
7
1
1 x
 x10
2
dx
0
22
 5
sin x

 cos x dx 
 log x 3 
#35 in your book:   2  dx 
 x 


23
Homework #2 is posted on my website; due in Lab on Monday.
Work on EMCF right after class.
Did you take Test 1? Practice Test 1? Quiz 1?
24