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3 years ago

Can someone tell me the answer to this???

Mathematics

1 answer:

MaRussiya [10]3 years ago

3 0

Option C is the correct answer of the question

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

Leni [432]

Answer: $\dfrac{2x^2-1}{x(x^2-1)}$

Step-by-step explanation:

The given function : $y=\ln(x(x^2 - 1)^{\frac{1}{2}})$

$\Rightarrow\ y=\ln x+\ln (x^2-1)^{\frac{1}{2}}$ [ $\because \ln(ab)=\ln a +\ln b$ ]

$\Rightarrow y=\ln x+\dfrac{1}{2}\ln (x^2-1)}$ [ $\because \ln(a)^n=n\ln a$ ]

Now , Differentiate both sides with respect to x , we will get

$\dfrac{dy}{dx}=\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})\dfrac{d}{dx}(x^2-1)$ (By Chain rule)

[Note : $\dfrac{d}{dx}(\ln x)=\dfrac{1}{x}$ ]

$\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})(2x-0)$

[ $\because \dfrac{d}{dx}(x^n)=nx^{n-1}$ ]

$=\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})(2x) = \dfrac{1}{x}+\dfrac{x}{x^2-1}\\\\\\=\dfrac{(x^2-1)+(x^2)}{x(x^2-1)}\\\\\\=\dfrac{2x^2-1}{x(x^2-1)}$

Hence, the derivative of the given function is $\dfrac{2x^2-1}{x(x^2-1)}$ .

8 0

4 years ago

Name the regular polygon that has 12 sides

AnnZ [28]

Answer:

dodecagon

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

If f and g are functions of time, and at time t = 2, f equals 5 and is rising at a rate of 6 units per second, and g equals 7 an

Yuliya22 [10]

Answer:

f/g at t =3 will be 9/8

d/ddx(f(x)/g(x))=f'(x)d(x)-f(x)g'(x)/(g'(x))^2

rate of change=(6*8)+(9*9)/9^2

rate of change =43/27=1.5925

8 0

3 years ago

Read 2 more answers

Mary earns $12.50 an hour cleaning houses if she works from 8:00 3:00 how much money will she make

irinina [24]

She earn 87.50 for that many hours

6 0

3 years ago

Read 2 more answers

During the first four months of the year, Jack earned $1270, $1150, $870 and $1450 If Jack must have an average salary of at lea

tia_tia [17]

Answer:

1010

Step-by-step explanation:

There are a whole class of questions that rely on the method to this one.

First add up what you know

1270 + 1150 + 870 + 1450 = 4740

Now add on the 5th month (which you don't know. Call it x)

4740 + x

Divide by 5

(4740 + x)/5 = 1150 and that is your equation

Solution

Multiply both sides by 5

5*(4740 + x) / 5 = 1150 * 5

4740 + x = 5750

Subtract 4740 from both sides

4740 - 4740 + x = 5750 - 4740

x = 1010

Which seems kind of low, but that's what the numbers come to.

6 0

3 years ago