MATHEMATICS COLLEGE

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.y = (ln x2)2

Answers

Answer 1

Answer:

Answer:

$(dy)/(dx)=(8lnx)/(x)$

Step-by-step explanation:

We are given that a function

$y=(lnx^2)^2$

We have to find the derivative of the function

Differentiate w.r.t x

$(dy)/(dx)=2(lnx^2)* (1)/(x^2)* 2x$

By using formula

$(d(lnx))/(dx)=(1)/(x)$

$(dx^n)/(dx)=nx^(n-1)$

$(dy)/(dx)=(4lnx^2)/(x)=(4(2)lnx)/(x)$

by using $lnx^y=ylnx$

Hence, the derivative of function

$(dy)/(dx)==(8lnx)/(x)$

Answer 2

Answer:

Answer: The required derivative is $(dy)/(dx)=\nfrac{4}{x\ln x^2}$

Step-by-step explanation:

Since we have given that

$y=(\ln x^2)^2$

We need to derivative it w.r.t 'x'., using "Chain rule"

As we know that

$(d)/(dx) \ln x=(1)/(x)\n\nand\n\n(d)/(dx)x^n=nx^(n-1)$

So, it becomes,

$(dy)/(dx)=(1)/(\ln (x^2)^2)* 2\ln(x^2)* (1)/(x^2)* 2x\n\n(dy)/(dx)=(4)/(x\ln x^2)$

Hence, the required derivative is $(dy)/(dx)=\nfrac{4}{x\ln x^2}$

Related Questions

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What is the factored form of 27d^6 + 8g^12

2.Make up a new pair of numbers that would make
the same shade of green. Explain how you know
they would make the same shade of green.

Answers

9514 1404 393

Answer:

29, 145

Step-by-step explanation:

Any pair of numbers with a ratio of 1 to 5 can be used. Some possible pairs are ...

3 : 15

4 : 20

29 : 145

The color depends on the ratio of blue to yellow paint. As long as that ratio is maintained, the color will be maintained.

This year, a small business had a total revenue of $81,900 . If this is 26% more than their total revenue the previous year, what was their total revenue the previous year?

Answers

Answer:

total revenue was $65,000

Step-by-step explanation:

A small business had a total revenue this year = $81,900

This is 26% more than their total revenue the previous year.

Let the revenue of previous year be 'r'.

r + ( 26% of r ) = $81,900

r + ( 0.26r ) = 81,900

1.26r = 81,900

r = $(81,900)/(1.26)$

r = 65,000

Their total revenue was $65,000 the previous year.

$65000 was the total revenue for the previous year.
65000 x .26 = 16900
65000 + 16900 = 81,900

Simplify by combining like terms- 9a+3-2a

Answers

Answer: 7a+3

Step-by-step explanation:

9a and 2a are two like terms that we can combine. Because there is a minus sign in front of the 2a, we should subtract 9a from 2a to get

7a. Then because the 3 has plus sign in front of it, we add 7a to 3. BUT because 3 a is NOT a like term, you don’t actually add it, so it looks like this: 7a+3. Hope this helped!

7a+3 because the 9 and 2 are from the same family since they both have a so u combine then and u cant combine 3 with anything so that’s left over

Sharon needs 64 credits to graduate from her couch she has 24 credits what percent of the required credits does she have

Answers

i think you do 24/64 = x/100 so you cross multiply and get 37.5%. idk if that is what you're looking for but i hope this helped

Answer:

Her proportion does not have corresponding parts in the same position.

Step-by-step explanation:

Line A y= 2x + 3 is parallel to another line B, what is the slope of the line B?

Answers

Answer:

Step-by-step explanation:

Since the lines are parallel, then the slope of line B would be the same as line A.

You have 137.26 in a bank account. The bank requires you to have at least 50$ in your account or else you are charged a fee. Write and solve an inequality that represents the amount you can write for your next check for without being charged

Answers

The inequality represents the amount you can check for without being charged is x + 50 ≤ 137.26 and its solution is x ≤ $87.26.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

You have 137.26 dollars in your bank account. If you do not have at least $50 in your account, you will be charged a fee.

Let x be the amount of can be taken from the account without being charged.

x + 50 ≤ 137.26

Simplify the inequality, then the value of 'x' will be

x + 50 ≤ 137.26

x ≤ 137.26 - 50

x ≤ $87.26

The inequality represents the amount you can check for without being charged is x + 50 ≤ 137.26 and its solution is x ≤ $87.26.

More about the inequality link is given below.

brainly.com/question/19491153

#SPJ2

Answer: x ≤ 87.26