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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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arlik [135]

Answer:

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Step-by-step explanation:

Given a correlation coefficient of -.11 the correlation would be extremely weak therefore it would have almost no correlation or causation

Why? Well when the value of the correlation is between -.1 and .1 then the relationship is said to have no correlation

-.11 is very close to -.1 thus meaning it would have pretty much no correlation

3 0
3 years ago
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A ball is shot upward from a slingshot at a velocity of 15 m/s the height of the ball after t seconds is given by h(t)=10+ 5t+1/
otez555 [7]

Answer:

The instantaneous velocity after eight seconds is 9 m/s

Step-by-step explanation:

Given as :

The ball shot upward with velocity of 15 m/s

The height of the ball after t sec is given as h(t) = 10 + 5t + \frac{1}{4}t^{2}

Now, The instantaneous velocity after 8 sec = \frac{\partial h(t)}{\partial t}

Or, The instantaneous velocity = \frac{\partial (10 +5t + \frac{1}{4}t^{2})}{\partial t}

or, The instantaneous velocity = 5 + \frac{1}{4}\times 2 t

Now at t = 8 sec

The instantaneous velocity = 5 + 4 = 9 m/s

Hence The instantaneous velocity of ball at t = 8 sec , is 9 m/s  Answer

3 0
3 years ago
Eight years ago, twice Manuel's age was 36. What is Manuel's age now? Pls hell
laila [671]

Answer:

Hey there!

Eight years ago, Manuel's age was 36/2, or 18.

Now, his age is 18+8, or 26 years old.

So, he is 26 years old now.

Hope this helps :)

8 0
3 years ago
Normally a new cell phone costs $500 you only have 450 to spend what happened what percent do you need the phone to be discounte
alina1380 [7]
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Theo bought 2 hot dogs and two drinks for $4.00. At the same concession stand, Vicky bought 3 hot dogs and a drink for $4.50. Wr
Sedbober [7]

Answer:

The hot dog are $2.63

Step-by-step explanation:

Hot Dogs = H

Drinks = D

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Divide both sides by 2

H + D = 2

Subtract D from either side

H = 2 -D

3H + D = 4.50

Plug in 2 - D for H

3(2- D ) + D = 4.50

6 - 3D + D = 4.50

6 - 4D = 4.50

Add 6 to either side

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Divide either side by -4

D = -2 . 625

3 0
3 years ago
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