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
What is the slope of the line that passes through the points (7.-12) and (-9,36)?​
REY [17]

Answer:

Step-by-step explanation:

m = slope where

m = rise / run

rise = y2 - y1  

run = x2 - x1

where  

the given point P1 = (7, -12)

and is in the form of (x1,y1)  

and

the given point P2 = (-9,36)  

is  in   the   form  of   (x2,y2)

then

m =  ( y2 - y1 ) / ( x2 - x1 )

m = ( 36 - (-12) ) / ( -9 -7 )

m = ( 36 + 12 ) /  ( - 16 )

m =  48 /  - 16

m = - 3

the slope is negative 3

slope = - 3

4 0
3 years ago
Please help meee, I’m having trouble in math. I solved the answer but got none of these.
tino4ka555 [31]
The answer is C

2.5 + 3.4 = 5.9

So:

5.9 x 10^4
6 0
3 years ago
Log (x) + log (x + 5) = log (6 x + 12) <br><br> I need the answer asap
kiruha [24]
It’s b I had it in my test
5 0
3 years ago
Read 2 more answers
Which matrix represents the system of equations shown below?
Leona [35]

Answer:

121-22

Step-by-step explanation:

7 0
3 years ago
Is a shoe store was having a back-to-school sale where you can buy six pairs of shoes for $52.62 if a large family decided to bu
hodyreva [135]
The family would buy the three pairs of shoes for $26.31 because you have to divide $52.62 in half since they bought half the amount of pairs of shoes that are given in the sale.
5 0
3 years ago
Other questions:
  • Can someone personally help me with geometry and area? Please I have more questions like that
    9·2 answers
  • Which one of the following foods is an example of a healthy dessert treat?
    13·2 answers
  • Solve the quadratic function by completing the square 2x^2+8x+14=0
    15·1 answer
  • Help! Help! Help! Help!
    13·1 answer
  • Math SAT: Suppose the national mean SAT score in mathematics was 510. In a random sample of 50 graduates from Stevens High, the
    8·1 answer
  • TU has endpoints at T(5, 11) and U(-4, -1). How long is TU?<br> Please help me
    12·1 answer
  • In 2014, a toy store sold 11,831 stuffed animals. In 2015, the toy store sold 13,170 more stuffed animals than it did in 2014. T
    11·1 answer
  • Anybody help me please!!!!!!!!!!!!!!!
    7·1 answer
  • The diagram shows the locations of Cody and Reese after running
    12·2 answers
  • Y=-5/4x-1 what is the slope and y intercept
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!