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
kicyunya [14]
3 years ago
14

Differentiating a Logarithmic Function In Exercise, find the derivative of the function

Mathematics
1 answer:
faust18 [17]3 years ago
4 0

Answer:  \dfrac{x^2}{(x^3+1)}

Step-by-step explanation

Properties of derivative , we use here :

  • \dfrac{d}{dx}(\ln x)=\dfrac{1}{x}
  • \dfrac{d}{dx}(x^n)=n(x)^{n-1}
  • \dfrac{d}{dx}(a)=0 , where a is constant.

The given function : y=\ln(x^3+1)^{\frac{1}{3}}

y=\dfrac{1}{3}\cdot \ln (x^3+1)  [\because n\ln x=\ln x^n]

Now , Differentiate both sides , we get

\dfrac{dy}{dx}=\dfrac{1}{3}\cdot \dfrac{1}{(x^3+1)}\cdot \dfrac{d}{dx}(x^3+1)

(By chain rule)

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

=\dfrac{1}{3}\cdot \dfrac{1}{(x^3+1)}(3x^2)

=\dfrac{x^2}{(x^3+1)}

Hence, the derivative of the function will be : \dfrac{x^2}{(x^3+1)}

You might be interested in
A = 1/2(a+b)h <br> h=? <br> h= ? times ? / ?+?
slega [8]
H means multiplication
1/2 x (a+b) x h

h is height
5 0
3 years ago
The five new teachers at a school were surveyed. Is this sample of teachers at the school likely to be biased?
nordsb [41]

Answer:

yes because since they are new they are all going to have a different opinion on the school than other teachers thats been there for years

hope this helps

have a good day :)

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
PLEASE HELP!! Will mark brainlest!!
vlada-n [284]

Answer:

I'm not even lying, it's none of them ;-;

btw if you want, can you give me brainliest :((

7 0
3 years ago
Read 2 more answers
Kim buys a new shirt for $25.50. She has to pay 8% sales tax. How much tax will be paid?​
Ainat [17]
Tax she will pay would be $2.04
4 0
2 years ago
The sum of the interior angles of a polygon is 3960 degrees find the size of its exterior angles ​
strojnjashka [21]

Answer:

4320 degrees

Step-by-step explanation:

If interior angles are 3960 degrees then there are 24 sides. If polygon is regular, size of each exterior angle is 15 degrees.

A polygon has as many pairs of interior and exterior as number of its sides. Further each pair of exterior and interior add up to

180 degrees.

Sum of all the exterior angles of any polygon is

360 degrees

As sum of all the interior angles of the polygon is

3960 degrees

Sum of all pairs of exterior and interior angles is

3960 degrees + 360degrees = 4320 degrees

5 0
3 years ago
Other questions:
  • A pizza shop charged $49.57 for 3 large pepperoni pizzas. This price included a $2.50 delivery fee.
    14·2 answers
  • Alyssa took a math test with 30 questions, and she answered 24 questions correctly in order to get an a, she needs to answer at
    8·1 answer
  • Find 0.45 of 80 A.36 B.3.6 C.0.36 D.0.036
    6·1 answer
  • MARK AS BRAINLIEST <br> 11+4-3/4
    5·2 answers
  • You are working for a company that creates tubes that measure 10 cm long and have a diameter of 6 cm. The tubes need to be cut j
    6·1 answer
  • Solve for x. −12x+13&gt;35 Drag and drop a number or symbol into each box to correctly complete the solution.
    7·1 answer
  • A project has an initial cash outflow of $19,927 and produces cash inflows of $17,329, $19,792, and $23,339 for Years 1 through
    12·1 answer
  • Yoshiko is a real estate agent. This
    15·1 answer
  • Find the slope for this relatioonship
    6·1 answer
  • PLEASE HELP ME !!! 5. Jack is choosing between two pest control companies, Mouse Arrest and Hugs, not Bugs. The amount that the
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!