Derivative Rules Flashcards
(40 cards)
1
Q
F(x): extrema
A
F’x: x-intercepts
2
Q
Fx: POI
A
F’x: extrema
3
Q
F’x: extrema
A
F’’x: X-intercepts
4
Q
Fx: decreasing
A
F’x: negative
5
Q
Fx: increasing
A
F’x: positive
6
Q
Fx: concave up
A
F’x: increasing
7
Q
F’x: increasing
A
F’’x: positive
8
Q
Fx: concave down
A
F’x: decreasing
9
Q
F’x: decreasing
A
F’’x: negative
10
Q
Fx: zero is maximum
A
F’x: + to -
11
Q
Fx: zero is minimum
A
F’x: - to +
12
Q
Fx: POI with horizontal tangent
A
F’x: +to + or - to -
13
Q
F’x: +to+ or - to -
A
F’’x: x intercept
14
Q
Fx: x^n
A
F’x: nx^n-1
15
Q
Fx: sinX
A
F’x: cosX
16
Q
Fx: cosX
A
F’x: -sinx
17
Q
Fx +- gx
A
F’x +- g’x
18
Q
KX
A
K
19
Q
K
A
0
20
Q
Kfx
A
Kf’x
21
Q
X^1/2
A
1/(2x^1/2)
22
Q
A^x
A
A^x•lnA
23
Q
E^x
A
E^x
24
Q
F(gx)
A
F’(gx)•g’x
25
E^-x
-e^-x
26
Fx•gx
Gx•f’x + fx•g’x
27
Fx/gx
(Gx•f’x- fx•g’x)/gx^2
28
1/x
-1/x^2
29
Tanx
1/cos^2x or sec^2x
30
F-1x
1/f’(f-1x)
31
Lnx
1/x
32
Cos-1x or arccos
-1/(1-x^2)^1/2
33
Sin-1x or arcsin
1/(1-x^2)^1/2
34
Tan-1x or arctan
1/(1-x^2)
35
E^kx
KE^kx
36
XY
Y+x(dy/dx)
37
X/Y
(Y-X(dy/dx))/Y^2
38
Cotx or 1/tan
-csc^2x
39
Secx or 1/cosx
Secxtanx
40
Cscx or 1/sinx
-cscxcotx
