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arsen [322]
3 years ago
13

What is the first and second derivative of xe^(2x)?

Mathematics
2 answers:
astra-53 [7]3 years ago
6 0
The derivative of a function <span>xe^(2x) can be determined by applying differential calculus techniques to the equation. In this case, the applicable law is the law of products

</span><span>y = xe^(2x)
y' = 2x  e^2x + e^2x
y'' = 4x e^2x + 2e^2x + 2 e^2x
Simplifying
y'' = (4x+4) e^2x </span>
Nimfa-mama [501]3 years ago
5 0
f(x)=xe^{2x}\\\\f'(x)=x'e^{2x}+x(e^{2x})'=e^{2x}+xe^{2x}\cdot2=2xe^{2x}+e^{2x}=e^{2x}(2x+1)\\\\f''(x)=(e^{2x})'(2x+1)+e^{2x}(2x+1)'=e^{2x}\cdot2(2x+1)+e^{2x}\cdot2\\\\=e^{2x}(4x+2)+2e^{2x}=(4x+2+2)e^{2x}=(4x+4)e^{2x}\\\\Answer:\\\boxed{f'(x)=(2x+1)e^{2x}\ and\ f''(x)=(4x+4)e^{2x}}
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3 years ago
Jason and Yolanda both drew a simple random sample from a non-normally distributed population of 25,000. Jason’s sample consiste
Ksenya-84 [330]

Both the sample can be used to make inferences about the population.

The correct option is D.

Given

Jason and Yolanda both drew a simple random sample from a non-normally distributed population of 25,000.

Jason’s sample consisted of 0.24% of the population, while Yolanda’s sample consisted of 0.32% of the population.

<h3>Percentage;</h3>

A percentage is a number or ratio that can be expressed as a fraction of 100.

According to the question

Total number of population = 25000

Percent of a sample of Jason = 0.24%

Percent of the sample of Yolanda's = 0.32%

So, the number of the population according to Jason's sample is given by;

=\dfrac{0.24}{100}\times 25000\\\\=0.24 \times 250\\\\=60

The number of the population according to Yolanda's sample is given by;

=\dfrac{0.32}{100}\times 25000\\\\=0.32 \times 250\\\\=80

Hence, Both the sample can be used to make inferences about the population

To know more about the percentage click the link given below.

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2 years ago
How many possible combinations of 6 numbers?
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3 years ago
Working together, two ants named Aran and Beatrice can build an ant hill in 10 hours. Aran and Charlie can build the ant hill in
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Step-by-step explanation:

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3 years ago
Four more than -3 times a number is equal to 8 more than -4 times the same number
postnew [5]

Answer:

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Explanation:

Let us call the number  

x

and write our condition as:

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rearranging: 4 x − 3 x = 8 − 4

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3 years ago
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