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Question 1 of 5
Find the derivative
y=e2x
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Substitute the components into the formula
ddx(ef(x)) |
= |
f′(x)⋅ef(x) |
|
|
= |
f′(2x)⋅e2x |
Substitute known values |
|
|
= |
2⋅e2x |
Differentiate 2x |
|
y’ |
= |
2e2x |
ddx(ef(x))=y’ |
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Question 2 of 5
Find the derivative
y=e4x+5
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Substitute the components into the formula
Differentiating constants makes them 0
ddx(ef(x)) |
= |
f′(x)⋅ef(x) |
|
|
= |
f′(4x)⋅e4x+5 |
Substitute known values |
|
= |
4⋅e4x+0 |
Differentiate 4x and 5 |
|
y’ |
= |
4e4x |
ddx(ef(x))=y’ |
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Question 3 of 5
Find the derivative
y=e-3x
Incorrect
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Substitute the components into the formula
ddx(ef(x)) |
= |
f′(x)⋅ef(x) |
|
|
= |
f′(−3x)⋅e−3x |
Substitute known values |
|
= |
−3⋅e−3x |
Differentiate -3x |
|
y’ |
= |
-3e-3x |
ddx(ef(x))=y’ |
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Question 4 of 5
Find the derivative
y=2e-x2
Incorrect
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Substitute the components into the formula
ddx(ef(x)) |
= |
f′(x)⋅ef(x) |
|
|
= |
f′(−x2)⋅2e−x2 |
Substitute known values |
|
|
= |
−12⋅2e−x2 |
Differentiate -x2 |
|
y’ |
= |
-e-x2 |
ddx(ef(x))=y’ |
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Question 5 of 5
Given that y=epx, find p
d2ydx2-dydx-6y=0
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First, find the first and second derivative of y
Substitute the components into the equation
d2ydx2−dydx−6y |
= |
0 |
|
p2epx−pepx−6epx |
= |
0 |
Substitute known values |
(p2epx-pepx-6epx)÷epx |
= |
0÷epx |
Divide both sides by epx |
p2-p-6 |
= |
0 |
Evaluate |
(p-3)(p+2) |
= |
0 |
Factorize |
Therefore, the value of p is 3 and -2.