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Paraphin [41]
2 years ago
12

The Leibnitz notation for the chain rule is

Mathematics
1 answer:
tankabanditka [31]2 years ago
6 0

For this derivative, you could set

\boxed{u = x^2 - 4x}

Then

y = \sin(x^2-4x) = \sin(u)

so that

\boxed{\dfrac{\mathrm dy}{\mathrm du} = \cos(u)}

and

\boxed{\dfrac{\mathrm du}{\mathrm dx} = 2x - 4}

Then the chain rule gives

\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{\mathrm dy}{\mathrm du}\dfrac{\mathrm du}{\mathrm dx} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = \cos(u)(2x-4) \\\\ \boxed{\dfrac{\mathrm dy}{\mathrm dx} = (2x-4)\cos(x^2-4x)}

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Please help i will give brainly :
Lubov Fominskaja [6]

1) The x-axis represents the energy (E), in joules. The y-axis represents the amplitude (x), in milimeters.

2) The curve depicts an <em>monotonous decrecent</em> rate of change.

3) The amplitude is directly proportional to the root square of the energy.

<h3>How to analyze a graph relationship between two variables</h3>

In this question we have a relationship between two variables, in which we must apply principles of <em>functional</em> analysis to respond three questions presented in the statement.

Now we proceed to answer the three questions below:

  1. <em>What is on the x-axis? The y-axis?</em> R/ The x-axis represents the energy (E), in joules. The y-axis represents the amplitude (x), in milimeters.
  2. <em>How would you describe the rate of change of the line?</em> R/ The curve depicts an <em>monotonous decrecent</em> rate of change, that is, the slope converges to zero when the energy tends to infinite.
  3. <em>What does this tell you about the relationship between amplitude and energy?</em> R/ The curve show a strong similarity with a function of the form x = A\cdot \sqrt{E}. Hence, the amplitude is directly proportional to the root square of the energy.

To learn more on functions, we kindly invite to check this verified question: brainly.com/question/12431044

5 0
2 years ago
How would the mean change if the number 52 replaced the number 12 in the set?
m_a_m_a [10]

Answer:

increase

Step-by-step explanation:

First, we need to find the mean of the given data set without any change.

10 + 61 + 10 + 44 + 21 + 79 + 27 + 12 = 264

264 ÷ 8 = <u>33</u>

Now that we have the mean, we can find the mean of the data set with the change of 52.

10 + 61 + 10 + 44 + 21 + 79 + 27 + 52 = 304

304 ÷ 8 = <u>38</u>

<u />

From this, we can see that the mean has increased with the change of 12 to 52. Thus, that's the correct option.

hope this helps!

6 0
2 years ago
Problem 1: 2x &gt; 4x - 6<br> problem 2: -3r &lt; 10 - r<br> problem 3: 5c - 4 &gt; 8c + 2
Trava [24]
<span>Problem 1: 2x > 4x - 6
                  2x < 6  
                    x < 3

problem 2: -3r < 10 - r
                   -2r < 10
                      r > -5

problem 3: 5c - 4 > 8c + 2
                       3c < -6
                         c < -2</span>
8 0
3 years ago
name the set of 6 consecutive integers starting with -3 put the set in braces and put commas between the elements of the set
melisa1 [442]
6-3=3 that is the answer ok
6 0
3 years ago
Kevin is 5 feet tall. Which proportion could you use to find the height of the flagpole? A. 3/5=12/x
dalvyx [7]
The answer is going to be A.

Shadow 1 / Height 1 = Shadow 2 / Height 2
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3 years ago
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