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MissTica
3 years ago
13

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

Mathematics
1 answer:
ludmilkaskok [199]3 years ago
8 0

Answer:

\dfrac{dy}{dx}=- \dfrac{1}{\left(x - 1\right) \left(x + 1\right)}

Step-by-step explanation:

Given:

y = \ln{\left(\dfrac{x + 1}{x - 1}\right)^{\frac{1}{2}}

using the properties of log we can take the power 1/2 and multiply it.

y = \dfrac{1}{2}\ln{\left(\dfrac{x + 1}{x - 1}\right)

now we can differentiate:

\dfrac{dy}{dx} = \dfrac{1}{2}\dfrac{1}{\left(\dfrac{x + 1}{x - 1}\right)}\left(\dfrac{d}{dx}\left(\dfrac{x+1}{x-1}\right)\right)

\dfrac{dy}{dx} = \dfrac{1}{2}\left(\dfrac{x - 1}{x + 1}\right)\left(- \dfrac{2}{\left(x - 1\right)^{2}}\right)

\dfrac{dy}{dx}=- \dfrac{1}{\left(x - 1\right) \left(x + 1\right)}

this is our answer!

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Find an<br> equation for the line through (-6, 3) and<br> parallel to y = 3x + 1.
Anika [276]

Since this line is parallel to y = 3x + 1 their slopes are equal. The slope is equal to 3. The line is also passing the point (-3,4).

This is the format of the line parallel to y = 3x + 1

y = 3x+ b

This line passes through point (-3, 4)

Replacing the values of y and x coming from the coordinates of (-3, 4)

4 = 3 * (-3) + b

Solving for the y-intercept b

4 = -9 + b

b = 4 + 9

b = 13

Knowing the slope as equal to 3 and the y-intercept as 13 the equation of the line is

y = 3x+13

7 0
3 years ago
25% of Rochelle's income is spent on rent. If Rochelle earns $1280 per week, how much is her weekly rent?
Neporo4naja [7]
25% of 1280
25/100 of 1280
1/4 of 1280
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7 0
2 years ago
Which of the following equations has a solution of x = -5?
polet [3.4K]

Answer:

B

Step-by-step explanation:

16(-5) - 7 = 11(-5) - 32

-80 - 7 = -55 - 32

-87 = -87

-4(-5) - 10 = 2(-5) + 20

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5 0
2 years ago
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A structure's reproduction cost new is $489,900. The structure has an effective age of 4 years and was built 10 years ago. Assum
olga_2 [115]

Answer:

Annual depreciation will be $32660

Step-by-step explanation:

We have given effective year = 4 years

Economic life = 60 years

Reproduction cost of the structure = $489900

We have to calculate the annual depreciation

Annual depreciation is given by

Annual depreciation =\frac{effective\ age}{economic\ life}\times reproduction\ cost=\frac{4}{60}\times 489900=$32660

So annual depreciation will be $32660

5 0
2 years ago
a scale model is made of a plane whose length is 114ft and whose wingspan is 95ft if the length of the model is 31 inches, find
Vlad [161]

Answer:

25.8

Step-by-step explanation:

114 ft ---> 31 inches

114 ft = 1368 inches

31/1368=0.02266081871 inch scale model

95 feet = 1140 inches, so 1140 * the scale factor of 0.02266081871= 25.83333..

This means, to the nearest tenth inch, the wingspan of the scale model is 25.8

6 0
3 years ago
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