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4. [/3 Points]
DETAILS
SCALCET9 2.XP.8.016.
Find the derivative of the function using the definition of derivative.
3
g(t) =
g(0)
ve
g'(t) =
State the domain of the function. (Enter your answer using interval notation.)
State the domain of its derivative. (Enter your answer using interval notation.)
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5
Dointel
STAI
CACETO 3 Y 2017
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5. [73 Points)
DETAILS
SCALCET9 2.XP.8.017.
Find the derivative of the function using the definition of derivative.
g(x) = 72*
g'(x) =
State the domain of the function. (Enter your answer using interval notation.)
State the domain of its derivative. (Enter your answer using interval notation.)
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6. [/3 Points]
DETAILS
SCALCET9 2.XP.8.014.
Find the derivative of the function using the definition of derivative.
6. [/3 Points]
DETAILS
SCALCET9 2.XP.8.014.
Find the derivative of the function using the definition of derivative.
1 – 4t
G(t)
6 +t
G'(t) =
State the domain of the function. (Enter your answer using interval notation.)
State the domain of its derivative. (Enter your answer using interval notation.)
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7. [12 Points]
DETAILS
SCALCET9 2.8.053.
Use the definition of derivative to find f'(x) and f”(x).
f(x) = 5x² + 8x + 1
Fl(x)
7. [12 Points]
DETAILS
SCALCET9 2.8.053.
Use the definition of derivative to find f'(x) and F”(x).
F(x) = 5×2 + 3x + 1
=
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8. [17 Points]
DETAILS
SCALCET9 2.8.059.
Show that the function f(x) = 5x – 2] is not differentiable at 2.
We have
if x 2 2
f(x) = (x – 2) =
if x < 2.
8. [17 Points]
DETAILS
SCALCET9 2.8.059.
Show that the function f(x) = (x  2] is not differentiable at 2.
We have
if x > 2
f(x) = (x – 2) =
if x < 2.
The righthand limit is
lim
f(x) – f(2)
X2
*27
and the lefthand limit is
f(x)  F(2)
X2
lim
X2
=
Since these limits are not equal, f'(2) = lim f(x) – f(2) does not exist and f is not differentiable at 2.
X2
x = 2
Find a formula for f' and sketch its graph.
if x = 2
f'(x) =
if x < 2
Graph Layers
7
6
After you add an object to the graph you
Craph layers to view and edit its
X2
EXISE and
X2
is not differentiable at 2.
Find a formula for f' and sketch its graph.
if x > 2
if x < 2
7
Graph Layers
6
5
5
After you add an object to the graph you
can use Graph Layers to view and edit its
properties.
4
نیا
3
Fill
2
1
7
6
4 3
2
1
5
2.
3
4
B
6
7
No
Solution
2
3
4
5
6
7
Help
WebAssign, Graphing Tool
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1. [/1 Points]
DETAILS
SCALCET9 3.XP.1.011.
Differentiate the function.
F(x) = 270
f'(x) =
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2. [11 Points]
DETAILS
SCALCET9 3.XP. 1.012.
Differentiate the function.
f(x) = 82
e
f'(x) =
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3. [/1 Points]
DETAILS
SCALCET9 3.1.003.
Differentiate the function,
g(x) = 3x + 4
g'(x) =
4. [/1 Points]
DETAILS
SCALCET9 3.1.006.MI.
Differentiate the function.
g(x) = x2 
 2x + 13
g'(x) =
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5. [/1 Points]
DETAILS
SCALCET9 3.1.019.MI.
Differentiate the function.
f(x) = x2(x + 6)
=
(+
f'(x) =
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6. [/1 Points]
DETAILS
SCALCET9 3.XP.1.015.
Differentiate the function.
g(t) = 4t3/8
g'(t) =
7. [/1 Points]
DETAILS
SCALCET9 3.XP.1.013.
Differentiate the function.
B(y) = cy  2
B'(Y) =
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8. [/1 Points]
DETAILS
SCALCET9 3.XP.1.014.
Differentiate the function.
FD=3
F(T) =
E'O) =
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9. [/1 Points]
DETAILS
SCALCET9 3.1.020.
Differentiate the function,
F(t) = (7t  4)2
F'(t) =
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WTEX
study
2022
https://www.webassign.net/web/Student/AssignmentResponses/last?dep=28710032
10. [/1 Points]
DETAILS
SCALCET9 3.XP. 1.030.
Differentiate the function.
h(t) = Vt  set
h'(t) =
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DETAILS
11. [/1 Points]
SCALCET9 3.1.021.MI.
ho
Differentiate the function.
5
y = 4e* +
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12. [/10 Points]
DETAILS
SCALCET9 3.1.033.MI.SA.
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the s
雞
study X
6 SOLU X
X
S 20220 X
6 20220 X
S20220 x
3.1 DE X
M My Bix
Modux
18 2022 x
www X
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M Home X
KE X
PEX
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12. [/10 Points)
DETAILS
SCALCET9 3.1.033.MI.SA.
MY NOTES
ASK YOUR TEACHER
PRACTICE A
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise
Differentiate the function.
7w2  5w + 3
y =
Vw
Step 1
7w?
The function y =
 5W + 3
ſw
is a quotient. It is important to remember that the derivative of a quotient F(W) is not the quotient of the derivatives P'(W) Instead, we find the derivative by first simplifying the quotient. We can rewrite it as follows:
g(w)
g'(w
7w²
Tw2
SW + 3
Sw
3
y =
+
VW
w
Remembering that w = w1/2 and that
= WNm, we will get the following:
wm
7w2
VW
7w
Sw
=
Sw
3w
SubmSkip you cannot come back)
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13. [/1 Points]
DETAILS
SCALCET9 3.1.038.
MY N
Msi
https://www.webassign.net/web/Student/AssignmentResponses/tutorial?dep=28710032&tags=autosave#question4763404_11
13. (/1 Points)
DETAILS
SCALCET9 3.1.038.
Find an equation of the tangent line to the curve at the given point.
y = 60° + x, (0.6)
y =
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DETAILS
14. (/2 Points]
SCALCET9 3.1.050.
Find the first and second derivative of the function.
G(r) = V8+ Vi
G'() =
GO)
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15. [14 Points]
DETAILS
SCALCET9 3.1.053.
The equation of motion of a particle is s = 12  12t, where s is measured in meters and t is in seconds. (Assume t2 0.)
Find the velocity and acceleration as functions of t.
Use the graph to determine
the xvalues at which fis discontinuous. For each xvalue, determine whether is continuous from the right, from the left, or neither.
у
f
X
2
4
6
Step 1
To find the numbers for which fis discontinuous, we look for xvalues for which the function is not defined or the left and right limits do not match.
Starting from the left and moving right, the first xvalue for which f(x) is discontinuous is x =
At this point, f(x) is not defined. Therefore, at this point fis which of the following?
continuous from the right
continuous from the left
neither
Step 2
Moving right, the next xvalue for which f(x) is discontinuous is x =
15. [14 Points]
DETAILS
SCALCET9 3.1.053.
The equation of motion of a particle is 5 =  120, where s is measured in meters and t is in seconds. (Assume t 20.)
(a) Find the velocity and acceleration as functions of t.
(c) =
a(t) =
(b) Find the acceleration, in m/s?, after 5 seconds.
m/s2
(c) Find the acceleration, in m/s2, when the velocity is 0.
m/s2
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16. [12 Points]
DETAILS
SCALCET9 3.1.059.
Find the points on the curve y = x3 + 3x2  9x + 4 where the tangent is horizontal.
smaller xvalue
(x,y) =
larger xvalue
(x,y) =
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17. [/1 Points)
DETAILS
SCALCET9 3.1.065.
Find an equation of the normal line to the curve of y = that is parallel to the line 6x + y = 1,
y =
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9. [13 Points]
DETAILS
SCALCET9 2.7.049.
MY NOTES
The cost (in dollars) of producing x units of a certain commodity is C(x) = 4,000 + 10x + 0.1x?
(a) Find the average rate of change (in $ per unit) of C with respect to x when the production level is changed from x = 100 to the given value. (Round your answers to the nearest cent.)
(0)
x = 104
$
per unit
(ii) x = 101
$
per unit
(b) Find the instantaneous rate
change (in $ per unit) of C with respect to x when x = 100. (This is called the marginal cost. Its significance will be explained in a future chapter.)
$
per unit
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10. [/6 Points]
DETAILS
SCALCET9 2.7.014.
MY NOTES
The displacement (in feet) of a particle moving in a straight line is given by s = 12  7t + 18, where t is measured in seconds.
(a) Find the average velocity (in ft/s) over each time interval.
(1) [4, 8]
ft/s
(ii) [6, 8]
Opera
Ift/s
It's here!
Instagram
the Opera
(iii) [8, 10)
Iftis
(iv) [8, 12]
si
Your last submission is used for your score.
1. [/2 Points]
DETAILS
SCALCET9 3.XP.5.003.
Consider the following equation.
4x2  y2 = 6
= 6
(a) Find y' by implicit differentiation.
y' =
(b) Solve the equation explicitly for y and differentiate to get y' in terms of x.
y' = +
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2. [/1 Points]
DETAILS
SCALCET9 3.5.005.MI.
dy
Find by implicit differentiation.
dx
x2  18xy + y2 = 18
dy
dx
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3. [/1 Points]
DETAILS
SCALCET9 3.5.009.
Find
by implicit differentiation.
dx
x2  y2 + 8
=
x + y
dx
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4. [11 Points]
DETAILS
SCALCET9 3.5.010.
dy
Find by implicit differentiation.
dx
xey = x  y
dy
dx
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5. [11 Points]
DETAILS
SCALCET9 3.5.015.MI.
dx
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5. [/1 Points]
DETAILS
SCALCET9 3.5.015.MI.
dy
Find
dx
by implicit differentiation.
y cos(x) = 3x2 + 5y2
=
dx
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6. [/1 Points]
DETAILS
SCALCET9 3.5.016.
dy
Find
by implicit differentiation.
dx
cos(xy) = sin(x + y)
+
dx
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新建标签页
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For this assignment, you submit answers by question parts. The numbe
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Your last submission is used for your score.
1. [0/1 Points]
DETAILS
PREVIOUS ANSWERS
SC.
Differentiate the function.
f(x) = 270
f'(x) = 702(69)
f(x
X
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2. [1/1 Points]
DETAILS
PREVIOUS ANSWERS
SC
Differentiate the function.
fly)  2.
新建标签
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4. Study pool  搜索
XS SOLUTION: mt15151....  Mat X
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11. [0/1 Points]
DETAILS
PREVIOUS ANSWERS
SCALCET
Differentiate the function.
5
y = 4e* + 31
37x
y' =
(3)
5.
=
40t +
X
3
X
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2. [3/10 Points]
DETAILS
PREVIOUS ANSWERS
SCALCET
This question has several parts that must be completed sequentially. If you
be able to come back to the skipped part.
raypal
* KONTAK
https://www.webassign.net/web/Student Assignment astep30710010
VW w
1
1/2
VW
3w
Step 2
Therefore, we have
7²  5W + 3
= 7w3/2 – Sw1/2 + 3w1/2
Vw
Now, since the function is a sum of power functions, we can use the Power Rule to find its derivative. Recall that according to the Power Rule, the derivative of w", where n is any real number is nw
To use the Power Rule, we'll have to calculate the following
3
2
1 =
1
1 =
12 / 2
1 =
Applying the power rule, we have the following.
w212 (1
w 112 + (1
])w3/2
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larger xvalue
(x, y)
1, 1
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 [0/1 Points]
DETAILS
PREVIOUS ANSWERS
SCALCET9 3.1.065.
Find an equation of the normal line to the curve of y =
✓x that is parallel to the line 6x + y = 1.
1
x+
y =
61
3
2
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11. [0/1 Points]
DETAILS
PREVIOUS ANSWER
Differentiate the function.
5
y = 4e* + 3
49
ho
VX
y' =
=
wollte
()
4e* – 5/3.x
X
X
CHP WUR
Road It
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Viewing Saved Work Revert to Last Response
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PREVIOUS ANSWE
12. [3/10 Points]
question4703404_11
Vw
Step 1
フルス
The function y =
 5w + 3
Vw
is a quotient. It is important to remember that the derivative of a quotient
Rw) is not the quotient of the derivatives (w), Instead, we find the derivative by first simplifying the quatient. We can reorite it as follows
(W)
g'(W)
7w2
3
Y
7w2  5w + 3
w
5w
Vw
+
ū
w
Remembering that w = w1/2 and that
=wnm, we will get the following.
wm
7w²
w
3/2
3/2
7w
5w
VW
1/2
Sw
wa
1/2
3w
1/2
Step 2
Therefore, we have
7w²  swt 3
VW
73/2  5w1/2 + 3w1/2
Rehtoate the following:
Now, since the function is a sum of power functions, we can use the Power Rule to find its derivative. Recall that according to the Power Rule, the derivative of w", where is any real number is
1/2
1 1/2
31
1/2
3/2
1312
3/2) 3,2
Applying the power rule, we have the following.
21/2 2112 wir
5/2
5/
21/2 + (3/2
v
Step 3
Now we can conclude the following.
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1. [12 Points)
DETAILS
SCALCET9 3.XP.5.003.
Consider the following equation.
4x² – ² = 6
(a) Find y' by implicit differentiation.
y
(b) Solve the equation explicitly for y and differentiate to get y' in terms of x.
y'=
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2. [/1 Points]
DETAILS
SCALCET9 3.5.005.MI.
Find
dy
by implicit differentiation.
dx
X2 – 18xy + y2 = 18
dy
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3. [11 Points]
DETAILS
SCALCET9 3.5.009.
Find by implicit differentiation,
dx
2 = 7+
xty
dy
dx
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4. [/1 Points]
DETAILS
SCALCET9 3.5.010.
dy
Find by implicit differentiation.
last dep=28710034
Find
dy
dx
by implicit differentiation.
xey = x  y
dy
dx
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5. 1/1 Points)
DETAILS
SCALCET9 3.5.015.MI.
Find
dx
en by implicit differentiation
y cos(x) = 3x2 + 5y2
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6. [/1 Points)
DETAILS
SCALCET9 3.5.016.
dy
Find by implicit differentiation.
뽑
cos(xy) = sin(x + y)
dy
dx
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7. [/1 Points)
DETAILS
SCALCET9 3.5.021.
dy
Find
dx
o by implicit differentiation,
eX/Y = 8x  y
dy
dx
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8. [/1 Points]
DETAILS
SCALCET9 3.XP.5.019.
Find
dy
by implicit differentiation.
dx
tan +(2x2y) = x + 3xy2
= X
dy
dx
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9. [/1 Points]
DETAILS
SCALCET9 3.XP.5.020.
Find
dy
by implicit differentiation.
dx
* sin(y) + y sin(x) = 1
dy
dx
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10. 1/1 Points]
DETAILS
SCALCET9 3.XP.5.021.
PLEASE
TO
WWW.DE
Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
y sin(12x) = x cos(2y), (1/2, 1/4)
y =
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11. [/1 Points]
DETAILS
SCALCET9 3.5.033.MI.
Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
*2 + y2 = (2x2 + 2y2 x)2 (
(cardioid)
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11. [/1 Points]
DETAILS
SCALCET9 3.5.033.MI.
Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
*2 + y2 = (2x2 + 2y3 – x)2 (0,5)
(cardioid)
y
0.5
х
0.5
0.5
1
0.5
CAL
BASULA
CAP
EL PEOR
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