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Igoryamba
3 years ago
6

How to solve for first derivative?? I have two questions, one where I have the answer, however one where I don’t. The format of

the answer must be similar to the first question. But how to find first derivative for second question?

Mathematics
1 answer:
rjkz [21]3 years ago
5 0

Answer:

Q1: f'(x) = (-6x^8 + 2x^4 + 4)(48x^7) + (6x^8)(-48x^7 + 8x^3)

Q2: f'(x) = (6x^4)(18x^2 - 54x^8) + (6x^3 - 6x^9 + 3)(24x^3)

Step-by-step explanation:

The derivative of the product of two functions is:

f(x) = v(x)u(x)

f'(x) = v(x)u'(x) + u(x)v'x)

The derivative is the product of the first function and the derivative of the second function added to the product of the second function and the derivative of the first function.

Q1: The function you are given is:

f(x) = 6x^8(-6x^8 + 2x^4 + 4)

You can think of that function as the product of functions

u(x) = 6x^8 and v(x) = -6x^8 + 2x^4 + 4

We first find the derivatives of functions u and v:

u'(x) = 48x^7 and v'(x) = -48x^7 + 8x^3

Now we follow the rule above:

f'(x) = v(x)u'(x) + u(x)v'x)

f'(x) = (6x^8)(-48x^7 + 8x^3) + (-6x^8 + 2x^4 + 4)(48x^7)

Use the commutative property to change the order of the sum.

f'(x) = (-6x^8 + 2x^4 + 4)(48x^7) + (6x^8)(-48x^7 + 8x^3)

This is the solution you have.

Q2: The function you are given is:

f(x) = 6x^4(6x^3 - 6x^9 + 3)

You can think of that function as the product of functions

u(x) = 6x^4 and v(x) = 6x^3 - 6x^9 + 3

We first find the derivatives of functions u and v:

u'(x) = 24x^3 and v'(x) = 18x^2 - 54x^8

Now we follow the rule above:

f'(x) = v(x)u'(x) + u(x)v'x)

f'(x) = (6x^4)(18x^2 - 54x^8) + (6x^3 - 6x^9 + 3)(24x^3)

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Here is your answer

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REASON:

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and,

(8-11)

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Hence,

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HOPE IT IS USEFUL

4 0
3 years ago
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Vsevolod [243]
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3 years ago
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if £2000 is placed into a bank account the pays 3percent compound interest per year, how much will be in the account after 2 yea
Nastasia [14]

Answer:

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8 0
3 years ago
Given six distinct pairs of gloves, 12 distinct gloves in all, how many ways are there to distribute two gloves to each of six s
noname [10]

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C(12, 2)

then I asked how many ways could the sets of gloves be assigned amongst the 6 sisters:

<span><span>6!</span><span>6!</span></span>

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using this same idea except:

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Talja [164]

Answer:

35/80

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there can be several answers to this...such as 35/80 reduces to 7/16...so 7/16 is proportional....or if u multiply numerator and denominator by the same number, u will find a proportional number...

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