1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
notsponge [240]
3 years ago
10

In Exercise, find the derivative of the function. y = ln(3 + x2)

Mathematics
1 answer:
erastovalidia [21]3 years ago
5 0

Answer:  \dfrac{2x}{3 + x^2}

Step-by-step explanation:

We know the property of derivative: \dfrac{d}{dx}(\log (x))=\dfrac{1}{x}

Given function : y=\ln(3 + x^2)

Differentiate both sides with respect to x , we get

\dfrac{dy}{dx}=\dfrac{d}{dx}(\ln(3 + x^2))

\Rightarrow\ \dfrac{dy}{dx}=\dfrac{1}{3 + x^2}\cdot\dfrac{d}{dx}(3 + x^2)  [By Chain rule]

\Rightarrow\ \dfrac{dy}{dx}=\dfrac{1}{3 + x^2}\cdot(0+2x)

[Since \dfrac{d}{dx}(a)=0 , where a is scalar and \dfrac{d}{dx}(x^n)=n(x)^{n-1}]

\Rightarrow\ \dfrac{dy}{dx}=\dfrac{2x}{3 + x^2}

Hence, the derivative of the given function is \dfrac{2x}{3 + x^2} .

You might be interested in
Is the equation 8 + 4= -5 + 7 true false or open and why
zysi [14]
This is false, because the equation is then 12=2, which is incorrect.

Hope this helps!

~ThePirc
4 0
2 years ago
Read 2 more answers
The cost of a car rental is ​40$ per day plus 20 cents per mile. You are on a daily budget of ​92$. Write and solve an inequalit
Ipatiy [6.2K]

Answer:

92-40=52

52/0.2 (0.2 = 20 cents) = 260

Step-by-step explanation:

260 is the greatest distance you can travel.

6 0
2 years ago
Help ineed to find this.
omeli [17]
She saved up a total of $82.60, and had to spend a total of $60.90, so she would have $21.70 left and need to save up another $180.40, hope this helps
5 0
3 years ago
Read 2 more answers
Please help asap 23 pts
Colt1911 [192]

That would be point E since it is between 1 and 2 on the number line and is a little bit closer to 2. hope this helps

3 0
3 years ago
Read 2 more answers
Shrinivas deposited $1300 in an account which pays 8% annual interest, compounded continuously. How long will it take to reach $
sertanlavr [38]

Answer: a. 12.4 years

Step-by-step explanation:

Function to represent exponential growth continuously:

A=A_0e^{rt}  ...(i)

, where A_0 = initial amount, r= rate of interest ( in decimal) , A = Amount after t years.

As per given , we have

A_0=\$1300\\\\r=8\%=0.08\\\\ A=\$3500

To find : t

Put all values in (i) ,

3500=(1300)e^{0.08t}\\\\\Rightarrow\ 2.6923077=e^{0.08t}

Taking natural log on both sides

\ln(2.6923076)= 0.08t\\\\\Rightarrow\ 0.99039867=0.08t\\\\\Rightarrow\ t=\dfrac{0.99039866}{0.08}=12.37998325\approx12.4

Hence, it would take <u>12.4</u> years.

so, the correct option is a. 12.4 years .

8 0
3 years ago
Other questions:
  • Write the number 78 as a product of its prime factors
    9·2 answers
  • Luna Ray has five orange picks and no green picks. You add some green picks do 1 in every 3 picks is orange . How many picks are
    8·1 answer
  • An airplane travels 2748 miles in 6 hours.How far would they travel in 2 hours?
    6·2 answers
  • What is the last digit of
    15·2 answers
  • Area = ???????????????
    12·1 answer
  • Hii this is geometry please help!!
    15·1 answer
  • Task 1: How do you get from one number to the next using multiplication or division?
    11·1 answer
  • A bunch of ballons contains many different colors. red 17 purple 11 orange 3 green 1 yellow 2 What is the probability that a ran
    8·1 answer
  • Are the two triangles​ similar? If​ yes, write a similarity statement and explain how you know they are similar.
    14·1 answer
  • Can someone check my answers to see if they are correct please? They are on the 2nd page. Thank you!
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!