Flashcards in Chapter 3.3-3.5 Deck (48)

Loading flashcards...

1

## what is a derivative of a constant?

### zero

2

## what is the power rule with and without a constant in front of the equation...

###
without: f(x) = x^n, then f'(x) = n x^n-1

with: f(x) = c x^n, then f'(x) =c n x^n-1

3

## what is the product rule?

### d/dx (uv)= (u'v+uv')

4

## what are all the other notation for the first derivative? (5)

###
1. f'(x)

2. dy/dx

3. d/dx y

4. d/dx f(x)

5. y'

5

## what are all the other notation for the second derivative? (3)

###
1. f''(x)

2. d^2y/dx

3. y''

6

## what do you do when it asks for the derivative of pi?

###
it is just zero

7

## what does "find the horizontal tangent(s)" mean?

### means find x when the derivative equation equals zero

8

## what does it mean when it asks for the slope of a tangent parallel to the x axis?

### slope is zero

9

## what equation do you use when it asks you to make an equation from slope and an ordered pair?

### y-y1 = m (x-x1)

10

## when the derivative curve is at y=0 what does this mean?

### this is a maximum or minimum of the original equation

11

## what is the derivative of sinx?

### cosx

12

## what is the derivative of cosx?

### -sinx

13

## what is the derivative of tanx?

### sec^2x

14

## what is the derivative of cscx?

### -cscx * cotx

15

## what is the derivative of secx?

### secx* tanx

16

## what is the derivative of cotx?

### -csc^2x

17

## position is (original equation, 1st derivative, 2nd derivative, or 3rd derivative?)

### original equation

18

## velocity is (original equation, 1st derivative, 2nd derivative, or 3rd derivative?)

### 1st derivative

19

## acceleration is (original equation, 1st derivative, 2nd derivative, or 3rd derivative?)

### 2nd derivative

20

## jerk is (original equation, 1st derivative, 2nd derivative, or 3rd derivative?)

### 3rd derivative

21

## what is the equation for displacement?

### change in s = f(change in time) -f(start time)

22

## what is the equation for average velocity?

### average velocity= (f(change in time) -f(start time))/ change in time

23

## what is the equation of speed?

### it is just the absolute value of the velocity equation

24

## when velocity hits zero what does this mean?

### means change in direction

25

## how do you know if a particle is moving to the left?

### negative velocity (negative slope)

26

## how do you know if a particle is moving to the right?

### positive velocity (positive slope)

27

## how do you know if a particle is standing still?

### when velocity is zero

28

## how do you know if a particle is speeding up?

### velocity and acceleration have the same sign

29

## how do you know if a particle is slowing down?

### velocity and acceleration have different signs

30