Section 1
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sec²(x)
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Last updated
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Date created
Mar 1, 2020
Cards (53)
Section 1
(50 cards)
sec²(x)
d/dx[uv]=
vu'+uv'
Exponential function
D: (-∞,+∞) R: (0,+∞)
Natural log function
D: (0,+∞) R: (-∞,+∞)
−1/2
cos(4π/3)
When is a object stopped?
v(t) = 0
Power Rule for Derivatives
When is an object slowing down?
a(t) and v(t) have different signs
cos(x)
Horizontal Asymptote
When does an object change direction?
v(t) changes sign
-1
cos(π)
When is an object moving left?
v(t) < 0
Average Acceleration
(Change in Velocity)/(Change in Time)
What does the graph y = sin(x) look like?
sec(x)tan(x)
√3/2
cos(π/6)
When is an object moving right?
v(t) > 0
1/2
cos(π/3)
−√2/2
cos(5π/4)
d/dx[secx]=
secxtanx
Square root function
D: (0,+∞) R: (0,+∞)
f'(g(x))g'(x)
d/dx[u/v]=
(vu'-uv')/v^2
f'(x)+g'(x)
−√3/2
cos(7π/6)
Extreme Value Theorem
If f is continuous on [a,b] then f has an absolute maximum and an absolute minimum on [a,b]. The global extrema occur at critical points in the interval or at endpoints of the interval.
Average Velocity
(Change in Position)/(Change in Time)
Reciprocal function
D: (-∞,+∞) x can't be zero R: (-∞,+∞) y can't be zero
vu'+uv'
Product Rule
d/dx[cscx]=
-cscxcotx
Cosine function
D: (-∞,+∞) R: [-1,1]
d/dx[cotx]=
-csc²x
Derivative with a coefficient rule
f'(x)-g'(x)
0
cos(3π/2)
Absolute value function
D: (-∞,+∞) R: [0,+∞)
Trig Identity: 1=
cos²x+sin²x
-csc²(x)
What does the graph y = tan(x) look like?
d/dx[tanx]=
sec²x
What does the graph y = cos(x) look like?
Sine function
D: (-∞,+∞) R: [-1,1]
d/dt[v(t)]=
a(t)
Mean Value Theorem
The instantaneous rate of change will equal the mean rate of change somewhere in the interval. Or, the tangent line will be parallel to the secant line.
√2/2
cos(π/4)
Limit Definition of a Derivative
-sin(x)
When is an object speeding up?
a(t) and v(t) have same sign
d/dt[s(t)]=
v(t)
Section 2
(3 cards)