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
NeTakaya
2 years ago
15

7-18 use part 1 of the fundamental theorem of calculus to find the derivative of the function.

Mathematics
1 answer:
blondinia [14]2 years ago
7 0

\displaystyle h(x)=\int\limits_{1}^{\sqrt{x}}~\cfrac{z^2}{z^4+1}dz~\hspace{10em}\cfrac{dh}{du}\cdot \stackrel{chain~rule}{\cfrac{du}{dx}\implies \cfrac{dh}{dx}} \\\\[-0.35em] ~\dotfill\\\\ u=\sqrt{x}\implies \cfrac{du}{dx}=\cfrac{1}{2\sqrt{x}} \\\\[-0.35em] ~\dotfill

\cfrac{dh}{dx}\implies \displaystyle \cfrac{d}{du}\left[ \int\limits_{1}^{u}~\cfrac{z^2}{z^4+1}dz \right]\cdot \cfrac{1}{2\sqrt{x}}\implies \left[ \cfrac{u^2}{u^4+1} \right]\cdot \cfrac{1}{2\sqrt{x}} \\\\\\ \stackrel{substituting~back}{\left[ \cfrac{(\sqrt{x})^2}{(\sqrt{x})^4+1} \right]\cdot \cfrac{1}{2\sqrt{x}}}\implies \cfrac{x}{x^2+1}\cdot \cfrac{1}{2\sqrt{x}}\implies \cfrac{\sqrt{x}}{2x^2+2}

You might be interested in
Find the measure of angle ABC
enot [183]
You will get x as 56 and angle ABC as 51°
4 0
3 years ago
Read 2 more answers
What is the measure of x? <br><br> A: 12<br> B: 9<br> C: 15<br> D: 6
ValentinkaMS [17]

Answer:

Your answer is

b.9

Mark my answer as brainlist . I need that urgently . Folow me for more answer.

Step-by-step explanation:

3 0
3 years ago
Give the appropriate theorem or postulate that can
vitfil [10]

Answer:

The right answer is A. AA Postulate

4 0
2 years ago
What is the constant of proportionality of $18.36 for 2 pizzas​
sergeinik [125]

Answer:

9.18

Step-by-step explanation:

7 0
3 years ago
Which is the best prediction for the number of pages in a chapter that takes 18 minutes to read?
mario62 [17]

Answer with explanation:

Time taken by a person to read number of pages in a chapter= 18 minutes

It is not given what is the length of the page.So,we can't say exactly  how many pages can a person read by completely understading what is written in each page in a chapter.

So, to fully understand each and every page in 18 minutes you can read minimum number of pages from the option given.

Option A:⇒ 15, is most appropriate.

9 0
3 years ago
Read 2 more answers
Other questions:
  • In a 5-day work week, Matt puts 175 miles on his car. His wife, Sarah, puts 100 more miles on her car than he does in the same a
    14·1 answer
  • What is the equation of the line that is perpendicular to the
    5·1 answer
  • Simplify the equation by combining
    5·2 answers
  • If it rained on 3 days out of 20 days on what percent of the days did it rain
    13·2 answers
  • A store donated 2 1/4 cases of crayons to a day care center. Each case holds 24 boxes of crayons; each box holds 8 crayons. How
    14·2 answers
  • Use the side spittler theorem to find x given that PQ |BC
    15·2 answers
  • John's collection of sports cards has 3/10 baseball cards and 39/100 football cards. the rest are soccer cards.what fraction of
    7·1 answer
  • The equation of a line is y=1/4x-2 What is the equation of the line that is parallel to the first line and passes through (4, –2
    9·1 answer
  • Find the rectangular coordinates of the point with the polar coordinates ordered pair negative 7 comma 5 pi divided by 3.
    14·1 answer
  • Eliana has 40$. she plans to save $25 every week to buy a plane ticket that costs $365. how many weeks will it take her to save
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!