Chapter 3.3-3.5 Flashcards
what is a derivative of a constant?
zero
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
what is the product rule?
d/dx (uv)= (u’v+uv’)
what are all the other notation for the first derivative? (5)
- f’(x)
- dy/dx
- d/dx y
- d/dx f(x)
- y’
what are all the other notation for the second derivative? (3)
- f’‘(x)
- d^2y/dx
- y’’
what do you do when it asks for the derivative of pi?
it is just zero
what does “find the horizontal tangent(s)” mean?
means find x when the derivative equation equals zero
what does it mean when it asks for the slope of a tangent parallel to the x axis?
slope is zero
what equation do you use when it asks you to make an equation from slope and an ordered pair?
y-y1 = m (x-x1)
when the derivative curve is at y=0 what does this mean?
this is a maximum or minimum of the original equation
what is the derivative of sinx?
cosx
what is the derivative of cosx?
-sinx
what is the derivative of tanx?
sec^2x
what is the derivative of cscx?
-cscx * cotx
what is the derivative of secx?
secx* tanx
what is the derivative of cotx?
-csc^2x
position is (original equation, 1st derivative, 2nd derivative, or 3rd derivative?)
original equation
velocity is (original equation, 1st derivative, 2nd derivative, or 3rd derivative?)
1st derivative
acceleration is (original equation, 1st derivative, 2nd derivative, or 3rd derivative?)
2nd derivative
jerk is (original equation, 1st derivative, 2nd derivative, or 3rd derivative?)
3rd derivative
what is the equation for displacement?
change in s = f(change in time) -f(start time)
what is the equation for average velocity?
average velocity= (f(change in time) -f(start time))/ change in time
what is the equation of speed?
it is just the absolute value of the velocity equation
when velocity hits zero what does this mean?
means change in direction
how do you know if a particle is moving to the left?
negative velocity (negative slope)
how do you know if a particle is moving to the right?
positive velocity (positive slope)
how do you know if a particle is standing still?
when velocity is zero
how do you know if a particle is speeding up?
velocity and acceleration have the same sign
how do you know if a particle is slowing down?
velocity and acceleration have different signs
cosx is the value of …
the x coordinate
sinx is the value of …
the y coordinate
what are the ordered pairs of 2pi?
( 1,0)
what are the ordered pairs of pi/6?
(“root 3”/2, 1/2)
what are the ordered pairs of pi/4?
(“root 2”/2, “root 2”/2)
what are the ordered pairs of pi/3?
(1/2, “root 3”/2)
what are the ordered pairs of pi/2?
(0,1)
what are the ordered pairs of 2pi/3?
(-1/2, “root 3”/2)
what are the ordered pairs of 3pi/4?
(“-root 2”/2, “root 2”/2)
what are the ordered pairs of 5pi/6?
(“-root 3”/2, 1/2)
what are the ordered pairs of pi?
(-1,0)
what are the ordered pairs of 7pi/6?
(“-root 3”/2, -1/2)
what are the ordered pairs of 5pi/4?
(“-root 2”/2, “-root 2”/2)
what are the ordered pairs of 4pi/3?
(-1/2, “-root 3”/2)
what are the ordered pairs of 3pi/2?
(0,-1)
what are the ordered pairs of 5pi/3?
(1/2, “-root 3”/2)
what are the ordered pairs of 7pi/4?
(“root 2”/2, “-root 2”/2)
what are the ordered pairs of 11pi/6?
(“root 3”/2, -1/2)
what is the quotient rule for finding derivative?
(u’v-uv’)/v^2
