Derivative Rules Flashcards

1
Q

F(x): extrema

A

F’x: x-intercepts

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Fx: POI

A

F’x: extrema

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

F’x: extrema

A

F’’x: X-intercepts

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Fx: decreasing

A

F’x: negative

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Fx: increasing

A

F’x: positive

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Fx: concave up

A

F’x: increasing

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

F’x: increasing

A

F’’x: positive

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Fx: concave down

A

F’x: decreasing

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

F’x: decreasing

A

F’’x: negative

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Fx: zero is maximum

A

F’x: + to -

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Fx: zero is minimum

A

F’x: - to +

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Fx: POI with horizontal tangent

A

F’x: +to + or - to -

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

F’x: +to+ or - to -

A

F’’x: x intercept

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

Fx: x^n

A

F’x: nx^n-1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

Fx: sinX

A

F’x: cosX

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Fx: cosX

A

F’x: -sinx

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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
Q

E^-x

A

-e^-x

26
Q

Fx•gx

A

Gx•f’x + fx•g’x

27
Q

Fx/gx

A

(Gx•f’x- fx•g’x)/gx^2

28
Q

1/x

A

-1/x^2

29
Q

Tanx

A

1/cos^2x or sec^2x

30
Q

F-1x

A

1/f’(f-1x)

31
Q

Lnx

A

1/x

32
Q

Cos-1x or arccos

A

-1/(1-x^2)^1/2

33
Q

Sin-1x or arcsin

A

1/(1-x^2)^1/2

34
Q

Tan-1x or arctan

A

1/(1-x^2)

35
Q

E^kx

A

KE^kx

36
Q

XY

A

Y+x(dy/dx)

37
Q

X/Y

A

(Y-X(dy/dx))/Y^2

38
Q

Cotx or 1/tan

A

-csc^2x

39
Q

Secx or 1/cosx

A

Secxtanx

40
Q

Cscx or 1/sinx

A

-cscxcotx