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
Naddik [55]
3 years ago
12

The derivative of (x^2 +1)(x^3+ 1) (by definition and basic rule)

Mathematics
1 answer:
dlinn [17]3 years ago
8 0

Answer:

f'(x) = 5x^4 + 2x + 3x^2

Step-by-step explanation:

To find the derivative of this equation we can do two things.

One method is to use the product rule, which states that when f(x) consists of two functions multiplied to each other (meaning f(x) = g(x) * h(x)), the derivative is f'(x) = g'(x)*h(x) + g(x)*h'(x). In simple language, the derivative is found by finding the derivative of x² + 1 and multiplying it with the normal function of x³ + 1, after which you add the product of the nnormal function of x² + 1 and the derivative of x³ + 1.

it might be clearer when I show you:

f(x) = (x^2 + 1)(x^3 + 1)\\f'(x) = (2x)(x^3 + 1) + (x^2 + 1)(3x^2)\\Simplify:\\f'(x) = 2x^4 + 2x + 3x^4 + 3x^2 = 5x^4 + 3x^2 + 2x\\

If you are not familiar with this rule you can first write out the function and then use the basic rule:

f(x) = (x^2 +1)(x^3+1) = x^5 + x^2 + x^3 + 1\\f'(x) = 5x^4 + 2x + 3x^2

If you need any further help please say so in the comments! I hope this helps! If the steps seem complicated, I suggest you could revise expanding brackets (the first step of the second method) and the basic rules of deriving, but feel free to reach out if you struggle afterwards still

You might be interested in
Find the domain and range of relation
Svetlanka [38]
Go find ppl who need answers and get more points that’s what I’m doing sorry
5 0
3 years ago
How many sides has an equiangular polygon if one of its exterior angles is 25 5/7?
lys-0071 [83]
Step One
Figure out the interior angle
25 5/7 = 25.714285 repeating. The interior angle is the supplement of this angle.

180 - 25.714285 = 154.2857
The formula relating the number of sides and the interior equal angle is

interior equal angle = 180 ( 1 - 2/n) where n is the number of sides. (Google equiangular polygon to find this formula.)

154.2857 / 180 = 1 - 2/n) 
0.8571428 = 6/7 = 1 - 2/n
1/7 = 2/n
n = 14 sides
This figure is regular as well as equiangular.
6 0
2 years ago
A survey shower that 82% of adults need correction for their eyesight. If 18 adults are randomly selected, find the probability
Ksju [112]

Answer: yes.

Step-by-step explanation:

18 people × .82 percent = 14.76

4 0
3 years ago
How many different committees of 4 people can be chosen from a group of 21?
sdas [7]

Answer:

There are 21 ways to choose the first person, 20 ways to choose the second, 19 ways for the third and 18 ways for the fourth so the answer is 21 * 20 * 19 * 18 = 143640.

4 0
3 years ago
Give an example of a rational function that has a horizontal asymptote at y = 0 and a vertical asymptote at
Vesnalui [34]
F(x)=x^2/(x-2)(x-1), the degree of the numerator and the degree of the denominator equal and the quotient of their coefficient equal to 1(horizontal asymptote means that the lines approach a certain number when the input approaches positive or negative infinity)
and when plugging in 2 or 1 as input, the output is undefined.
8 0
3 years ago
Read 2 more answers
Other questions:
  • In Mr.Ford’s class, 3 out of 25 students are left-handed. Whick of the following is the percent of “lefties” in Mr. Ford’s class
    15·2 answers
  • Given the polynomial function below , find F(2)
    6·2 answers
  • Which of the following is a geometric sequence with a common ratio of 2?
    6·1 answer
  • X + y&lt; 12<br> 3x - y&gt; -1<br> y20
    15·1 answer
  • Mark needs to cut a piece of glass to replace a broken window. He has four pieces of glass: 6 feet long, 5 feet long, 3 feet lon
    6·1 answer
  • Most fish can swim in water (T). Dogs are fish (F). So, Dogs can probably swim. This argument is
    8·1 answer
  • Raheen used a table to record the highest temperature in his town. Sunday was 80 degrees, Monday was 86, Tuesday was 90, Wednesd
    6·2 answers
  • What is 2 and 1/3+ 3 and 1/3
    5·1 answer
  • Evaluate 4a for a = 5 . Express your answer in simplest form.<br> 20<br> 22<br> 45<br> 20
    10·2 answers
  • Alicia buys a fish tank. The dimensions of the fish tank are 80 cm x 35cm x 40cm. Alicia fills the tank with water to 4/5 of the
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!