midterm 2 Flashcards
1
Q
Product rule [f(x)g(x)}
A
f(x)g’(x)+g(x)f’(x)
2
Q
Quotient rule [f(x)/g(x)]
A
g(x)f’(x)-f(x)g’(x)/g(x)^2
3
Q
Power rule [x^n]
A
nx^n-1
4
Q
Difference rule [f(x)-g(x)]
A
f’(x)-g’(x)
5
Q
Chain rule d/dx [f(g(x))]
A
f’(g(x))g’(x)
6
Q
Constant multiple [g(x) = C*f(x)]
A
C*f’(x)
7
Q
Sum rule [f(x)+g(x)]
A
f’(x)+g’(x)
8
Q
sinx
A
cosx
9
Q
cosx
A
-sinx
10
Q
tanx
A
sec^2x
11
Q
secx
A
secxtanx
12
Q
cotx
A
-csc^2x
13
Q
cscx
A
-cscxcotx
14
Q
tanx (identity)
A
sinx/cosx
15
Q
sin(ax)
A
acos(ax)
16
Q
cos(ax)
A
-asin(ax)
17
Q
a^x
A
ln(a)a^x
18
Q
e^x
A
e^x
19
Q
e^kx
A
ke^x
20
Q
lnx
A
1/x
21
Q
sin^-1x
A
1/sqrt(1-x^2)
22
Q
cos^-1x
A
-1/sqrt(1-x^2)
23
Q
tan^-1x
A
1/1+x^2
24
Q
cot^-1x
A
-1/1+x^2
25
sec^-1x
1/xsqrt(x^2-1)
26
csc^-1x
-1/xsqrt(x^2-1)
27
How do you find critical numbers?
set f'(x) = 0 and solve
28
how do you find where f(x) is increasing/decreasing?
evaluate f'(x) at intervals
29
how do you find inflection points?
set f''(x) = 0 and solve
30
How do you find relative extrema?
evaluate f(x) at increasing and decreasing intervals
31
how do you find absolute extrema?
evaluate f(x) at all intervals
32
l'Hospitals rule
if f(x)/g(x) = 0/0 or oo/oo the f'(x)/g'(x)
33
how do you find delta x?
b-a/n
34
What is the derivative of position?
velocity
35
What is the derivative of velocity?
acceleration
