A derivative is also ________________

the slope., the instantaneous rate of change., the instantaneous velocity.

f'(x) = [(2x5 + 2)(20x3) - (5x4)(10x4)] / (2x5 + 2)2, f'(x) = -(5x4)(2x5 + 2)-2(10x4) + (2x5 + 1)-1(20x3)

y' = x(x2 + 1)(-1/2), y' = (1/2)(x2 + 1)(-1/2) (2x)

dy/dx = -(4x3 +2x2)(3x2 + 3)-2(6x) + (3x2 + 3)-1(12x2), dy/dx = [(3x2 + 3)(12x2 +4x) - (4x3 +2x2)(6x)] / (3x2 + 3)2

dy/dx = dy/dx = -2(-5x2 + 3) (10x), dy/dx = 2(-5x2 + 3) (-10x)

y' = (x5 - 4x4 - 1)(-10x4) + (-2x5 +1)(5x4 - 16x3)

y' = (-3x4 - 5)(-20x3) + (-5x4 + 1)(-12x3), y' = 120x7 - 36x2 +100

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Basic Derivatives with vocabulary

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Questions 35

Answers

1
Find dy/dx.
dy/dx = (5x3 + 1)(15x4) - (3x5 + 1)(15x2)
dy/dx = (5x3 + 1)(15x4) + (3x5 + 1)(15x2)
dy/dx = (5x3 + 1)(15x4)(3x5 + 1)(15x2)
dy/dx = (5x3 + 1) + (3x5 + 1)
2
Find f'(x).
f'(x) = (5x4 + 1)+ (-3x5 - 4)
f'(x) = (-15x4) + (-3x5 - 4)
f'(x) = (5x4 + 1)(-15x4) + (-3x5 - 4)(20x3)
f'(x) = (5x4 + 1)(-15x4) - (-3x5 - 4)(20x3
3
A process that maximizes or minimizes some quantity to have the best fit.
differentiation
optimization
area
local extrema
4
Find y'.
y' = (-2x5)(5x4)(x5 - 2)(-10x4)
y' = (-2x5)(5x4) - (x5 - 2)(-10x4)
y' = (-2x5)(5x4) + (x5 - 2)(-10x4)
y' = -100x9 +20x4
5
the opposite of derivatives
Inverse
Limits
Velocity
integrals
6
A derivative is also ________________
the slope.
my worst nightmare.
the instantaneous rate of change.
the instantaneous velocity.
7
f=cos5x then F'(x)
-5sin5x
5cos5x
5tan5x
5sin5x
8
Who is the father of calculus
Euclid
Gottfried Leibniz
Pythagoras
Galileo
9
Find the derivative at the given value.
f'(-1) = 9
f'(-1) = -1
f'(-1) = 1
f'(-1) = 6
10
f= secx then F'(x)
sinxcosx
tanxcosx
secxsinx
secxtanx
11
Find f'(x).
f'(x) = [(2x5 + 2)(20x3) - (5x4)(10x4)] / (2x5 + 2)2
f'(x) = -(5x4)(2x5 + 2)-2(10x4) + (2x5 + 1)-1(20x3)
f'(x) = [(5x4)(10x4) - (2x5 + 2)(20x3)] / (2x5 + 2)2
f'(x) = [(2x5 + 2)(20x3) - (5x4)(10x4)] / (2x5 + 2)
12
The lowest point of a function.
absolute value
absolute minimum
critical point
minimum
13
Uh-oh. Where is this function NOT differentiable?
At x = 1.
At x = 0.
Nowhere! The graph is fine!
At x = 2.
14
The derivative is the _____________
average velocity.
instantaneous velocity.
speed.
average rate of change.
15
A part of the graph that looks like a frown.
turning point
concave up
concave down
constant function
16
Find y'.
y' = (1/2)(x2 + 1)(1/2) (2x)
y' = x(x2 + 1)(-1/2)
y' = (1/2)(x2 + 1)(-1/2) (2x)
y' = (1/2)(x2 + 1)(-1/2)
17
Find dy/dx.
dy/dx = 4(3x4 + 4)3 + 12x3
dy/dx = 4(12x3)3
dy/dx = 4(3x4 + 4)3
dy/dx = 4(3x4 + 4)3 (12x3)
18
Kanye west is
A GENUIS
an Idiot
19
Find dy/dx.
dy/dx = [(4x3 +2x2)(6x) - (3x2 + 3)(12x2 +4x)] / (3x2 + 3)2
dy/dx = -(4x3 +2x2)(3x2 + 3)-2(6x) + (3x2 + 3)-1(12x2)
dy/dx = [(3x2 + 3)(12x2 +4x) + (4x3 +2x2)(6x)] / (3x2 + 3)
dy/dx = [(3x2 + 3)(12x2 +4x) - (4x3 +2x2)(6x)] / (3x2 + 3)2
20
The Second Derivative
Rate of change
Velocity
Speed
Acceleration
21
f= sin2x f'(x)=
cos2x
2sincosx
2sin2x
2cos2x
22
Find y'.
y' = 12x3
y' = -12x3
y' = -3x3
y' = -4x4
23
Find y'.
y' = 3( 3x4 - 5)-4 (12x3)
y' = -3( 3x4 - 5)-2 (12x3)
y' = -3( 3x4 - 5)-4 (12x3)
y' = -3( 3x4 - 5)-2
24
Find dy/dx.
dy/dx = dy/dx = -2(-5x2 + 3) (10x)
dy/dx = 2(-5x2 + 3) + (-10x)
dy/dx = 2(-5x2 + 3) (-10x)
dy/dx = 2(-5x2 + 3) (10x)
25
Find y'.
y' = (x5 - 4x4 - 1)(-10x4) - (-2x5 +1)(5x4 - 16x3)
y' = (x5 - 4x4 - 1)(-10x4)(-2x5 +1)(5x4 - 16x3)
y' = (x5 - 4x4 - 1)(-10x4) + (-2x5 +1)(5x4 - 16x3)
y' = (-10x4) + (5x4 - 16x3)
26
The original function, for example s(t), is the ____________
time.
derivative.
position function.
instantaneous rate of change.
27
The first Derivative is the ___ of the initial function
Velocity
distance
Speed of sound
Speed of light
28
Determines whether a point is a minimum, maximum, or neither.
fourth derivative test
third derivative test
first derivative test
second derivative test
29
Find the derivative at the given value.
f' (3) = 13/2
f' (3) = 5/2
f'(3) = 3
f' (3) = 5
30
Where the function changes from concave up to concave down or vice versa.
critical point
maximum point
inflection point
minimum point
31
Find the derivative at the given value.
f'(3) = 4
f'(3) = 3
f'(3) = 45
f'(3) = -3
32
The slope of the tangent line
SUMS
area
derivatives
LIMITS
33
Find y'.
y' = 2x
y' = -2
y' = x
y' = 2
34
Find y'
y' = (-3x4 - 5)(-20x3) - (-5x4 + 1)(-12x3)
y' = (-3x4 - 5)(-20x3) + (-5x4 + 1)(-12x3)
y' = 120x7 - 36x2 +100
y' = (-3x4 - 5)+ (-5x4 + 1)
35
The rate of change (value of the derivative) at a particular moment.
instantaneous rate of change
instantaneous velocity
speed
velocity

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