Derivative Flashcards
1
Q
π
A
0
2
Q
x
A
1
3
Q
f(x) = 2x^3 - 5x^2 +3x -2
A
6x^2 - 10x +3
4
Q
f(x)g(x)
A
f’(x)g(x) + f(x)g’(x)
5
Q
f(x)/g(x)
A
(f’(x)g(x) - f(x)g’(x)) / (g(x)^2)
6
Q
f(x)^u
A
u(f(x)^u-1)(u’)
7
Q
Sinx
A
Cosx
8
Q
Cosx
A
-sinx
9
Q
Sin^2(x)
A
f(x) = (sinx)^2
f’(x) = 2sinxcosx
10
Q
√u
A
(1/2)u^(-1/2) u’
11
Q
e^u
A
(e^u) u’
12
Q
a^u
A
ln(a) (a^u) u’
13
Q
loga^u
A
(1/ u ln(a)) u’
14
Q
tanx
A
sec^2(x)
15
Q
csc(x)
A
-csc(x)cot(x)
16
Q
sec(x)
A
sec(x)tan(x)
17
Q
cot(x)
A
-csc^2(x)
18
Q
ln(u)
A
(1/u) u’
19
Q
ln(u)
A
(1/u) u’
20
Q
f(x) using a limit
A
(Lim h->0) (f(x-h) - f(x)) / h
21
Q
sin^-1(x)
A
1/√(1-x^2)
22
Q
cos^-1(x)
A
-1/√(1-x^2)
23
Q
tan^-1(x)
A
1/(1+ x^2)
24
Q
cot^-1(x)
A
-1/(1+ x^2)
25
csc^-1(x)
-1/(x√((x^2) -1))
26
sec^-1(x)
1/(x√((x^2) -1))
27
When to use squeeze theory
With trig
example: -1 < sinx < 1
28
|a| > x
-x > a > x
29
When to use l`hospital rule
0/0 or (+/-infinite)/(+/-infinite)
30
(d/dx)y^2 = (d/dx)x + (d/dx)5
(dy/dx)y = 1 + 0
31
L'hospital equation
(Lim x->a) f(x)/g(x) = (Lim x->a) f'(x)/g'(x)
32
L'hospital equation
(Lim x->a) f(x)/g(x) = (Lim x->a) f'(x)/g'(x)
