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Lemur [1.5K]
3 years ago
9

{ lnx } " align="absmiddle" class="latex-formula">
how do I differentiate this
Mathematics
1 answer:
Kamila [148]3 years ago
3 0

Use the power rule for differentiation:

\dfrac{\text{d}}{\text{d}x} (f(x))^k = k(f(x))^{k-1}f'(x)

You can use this formula if you remember that a root is just a rational exponential:

\sqrt[4]\ln(x) = (\ln(x))^{\frac{1}{4}}

So, remembering that the derivative of the logarithm is 1/x, you have

\dfrac{\text{d}}{\text{d}x} (\ln(x))^{\frac{1}{4}} = \frac{1}{4}(\ln(x))^{\frac{1}{4}-1}\dfrac{1}{x}

Which you can rewrite as

\dfrac{1}{4}(\ln(x))^{\frac{1}{4}-1}\dfrac{1}{x} =\dfrac{1}{4}(\ln(x))^{\frac{-3}{4}}\dfrac{1}{x} =\dfrac{1}{4}\dfrac{1}{\sqrt[4]{\ln(x))^3}}\dfrac{1}{x} = \dfrac{1}{4x\sqrt[4]{\ln(x))^3}}

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Answer:

it is the sum of the initial amount and the additional amount after d days

Step-by-step explanation:

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3 years ago
In a study of the relationship between pet ownership and physical activity in older adults, 586 subjects reported that they owne
hram777 [196]

Answer:

Step-by-step explanation:

In a study of the relationship between pet ownership and physical activity in older adults, 586 subjects reported that they owned a pet, while 1931 reported that they did not. Give a 98% confidence interval for the proportion of older adults in this population who are pet owners. Lower limit Incorrect: Your answer is incorrect. Upper limit

p ± z × (1 - p/n)

z = 98%

p = 586/1931

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n = 1931

Approximately = 0.3035

Confidence interval =

0.3035 + 2.326 × ( 1 - 0.3035/ 1931)

3 0
3 years ago
Translate and solve the algebraic statement for the given number below:
xenn [34]
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8 0
3 years ago
2x+3y=-27 is one equation in a coincidental system of two linear equations. the other equation is __y=__x-102.
Snezhnost [94]
Given:

An equation in a coincidental system of two linear equations:

2x + 3y = -27

The other equation is 

_y = _x - 102

Rearrange the second equation to be identical to the first

_y - _x = -102

Determine the factor, -102/-27 = 3.78

for x, 2 * 3.78 = 7.56
for y, 3 * 3.78 = 11.33

The second equation, 11.33y - 7.56x = -102
3 0
3 years ago
Find the x-intercepts for the parabola defined
Ulleksa [173]

Answer:

(- 2, 0 ), (1, 0 )

Step-by-step explanation:

Given

y = 2x² + 2x - 4

To find the x- intercepts let y = 0, that is

2x² + 2x - 4 = 0 ← divide through by 2

x² + x - 2 = 0 ← in standard form

(x + 2)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 1 = 0 ⇒ x = 1

Thus x- intercepts are (- 2, 0) and (1, 0)

5 0
3 years ago
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