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Question 1 of 5
Find the derivative
y=4-3e-x
Incorrect
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Substitute the components into the formula
Differentiating constants makes them 0
ddx(ef(x)) |
= |
f′(x)⋅ef(x) |
|
|
= |
4−f′(−x)⋅3e−x |
Substitute known values |
|
= |
0−(−1⋅3e−x) |
Differentiate -x and 4 |
|
y’ |
= |
-3e-x |
ddx(ef(x))=y’ |
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Question 2 of 5
Find the derivative
y=6ex2-3e-2x
Incorrect
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Progress: 0%
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Substitute the components into the formula
First Term:
ddx(ef(x)) |
= |
f′(x)⋅ef(x) |
|
|
= |
(f′(x2)⋅6ex2)−3e−2x |
Substitute known values |
|
|
= |
(12⋅6ex2)−3e−2x |
Diferrentiate x2 |
|
|
= |
3ex2-3e-2x |
Second Term:
|
= |
3ex2−(f′(−2x)⋅3e−2x) |
Substitute known values |
|
= |
3ex2−(−2⋅3e−2x) |
Diferrentiate -2x |
|
y’ |
= |
3ex2+6e-2x |
ddx(ef(x))=y’ |
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Question 3 of 5
Find the derivative
y=e2x+e-x2
Incorrect
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Separate the two terms by giving each a denominator of 2
Substitute the components into the formula
First Term:
ddx(ef(x)) |
= |
f′(x)⋅ef(x) |
|
|
= |
(f′(2x)⋅e2x2)+e−x2 |
Substitute known values |
|
|
= |
(2⋅e2x2)+e−x2 |
Diferrentiate 2x |
|
|
= |
e2x+e-x2 |
22=1 |
Second Term:
|
= |
e2x+(f′(−x)⋅e−x2) |
Substitute known values |
|
|
= |
e2x+(−1⋅e−x2) |
Differentiate -x |
|
y’ |
= |
e2x-e-x2 |
ddx(ef(x))=y’ |
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Question 4 of 5
Find the derivative
y=e3-2x2
Incorrect
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Progress: 0%
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Substitute the components into the formula
Differentiating constants makes them 0
ddx(ef(x)) |
= |
f′(x)⋅ef(x) |
|
|
= |
f′(3−2x2)⋅e3−2x2 |
Substitute known values |
|
= |
−4x⋅e3−2x2 |
Diferrentiate 3-2x2 |
|
y’ |
= |
-4xe3-2x2 |
ddx(ef(x))=y’ |
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Question 5 of 5
Find the derivative
y=e-0.03x
Incorrect
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Progress: 0%
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Substitute the components into the formula
ddx(ef(x)) |
= |
f′(x)⋅ef(x) |
|
|
= |
f′(−0.03x)⋅e−0.03x |
Substitute known values |
|
= |
−0.03⋅e−0.03x |
Diferrentiate -0.03x |
|
y’ |
= |
-0.03e-0.03x |
ddx(ef(x))=y’ |