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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

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114₅ = 25 + 5 + 4

114₅ = 34

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2 years ago
2 friends share 3 fruit bars equally. How much does each friend get?
gizmo_the_mogwai [7]
1.5 for each friend, plus who eats fruit bars xD
5 0
3 years ago
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15 cm<br> 4 cm<br> cm<br> V=____cm3
bonufazy [111]

Answer:

V=(πr^2 x h)/3

lets use π as 3.14 cause I dont know what pi u using

3.14 x 4^2 x 15 = 753.6/3 = 251.2

If you're using π as your pi, than just replace 3.14 by π on calculator

Hope that answers your question

8 0
3 years ago
Before conducting some experiments, a scientist mixes 1/2 gram of Substance A with 3/4 grams of Substance B. If the scientist us
Tju [1.3M]

Answer: 10

<u>Step-by-step explanation:</u>

 (\frac{1}{2}+\frac{3}{4})÷\frac{1}{8}

= (\frac{1}{2}(\frac{2}{2})+\frac{3}{4})÷\frac{1}{8}

= (\frac{2}{4}+\frac{3}{4})÷\frac{1}{8}

= (\frac{5}{4})÷\frac{1}{8}

= (\frac{5}{4})x\frac{8}{1}

= \frac{40}{4}

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4 0
3 years ago
Carla is collecting rainwater in a barrel. Currently she has 18 inches of water in the barrel. The rain is falling at the rate o
olga_2 [115]

Answer: it will take 9 hours.

Step-by-step explanation:

The rain is falling at the rate of 1.5 inches per hour. This means that the height of water in the barrel is increasing in arithmetic progression.

The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + d(n - 1)

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 18 inches

d = 1.5 inches

The expression becomes

Tn = 18 + 1.5(n - 1)

For the number of hours it would take to collect 30 inches of rain in the barrel, Tn = 30

Therefore,

30 = 18 + 1.5(n - 1)

1.5(n - 1) = 30 - 18

1.5(n - 1) = 12

n - 1 = 12/1.5 = 8

n = 8 + 1

n = 9

6 0
3 years ago
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