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docker41 [41]
2 years ago
8

Use the chain rule to find the derivative of each of the following :

Mathematics
1 answer:
ankoles [38]2 years ago
5 0

Answer:

see explanation

Step-by-step explanation:

Using the chain rule

Given

y = f(g(x)), then

\frac{dy}{dx} = f'(g(x)) × g'(x)

(a)

y = \frac{2}{(3x^2-x+7)^3} = 2 (3x^2-x+7)^{-3}

\frac{dy}{dx} = 2. - 3 (3x^2-x+7)^{-4} × \frac{d}{dx} (3x² - x + 7)

   = - 6 (3x^2-x+7)^{-4} × (6x - 1)

   = \frac{-6(6x-1)}{(3x^2-x+7)^4}

---------------------------------------------------

   (b)

y = (4x-10)^{10}

\frac{dy}{dx} = 10(4x-10)^{9} × \frac{d}{dx}(4x - 10)

    = 10(4x-10)^{9} × 4

     = 40(4x-10)^{9}

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What does the missing number represent?
kenny6666 [7]

Answer: (C) the number of groups

Step-by-step explanation: It cannot be the total because the total is 18, the size of the groups does not make sense because it seems that you are trying to find a total, and the difference makes no sense because this does not seem like a subtraction problem. (C) the number of groups makes sense because their is a total number of groups.

Hope this helps! :)

6 0
3 years ago
Read 2 more answers
Identify the ordered pair that represents the vector from A(-8,-1) to B(-5,3) and the magnitude of vector AB.
wel
In order to find the vector that points from A to B we need to subtract each component of A from the corresponding component of B, according to the formula: v(a→b)=(b1−a1,b2−a2) In this case we have : v(a→b)=(−5−(−8),3−(−1)) <span>v(a→b)=(3,4)

</span>To find the magnitude we use the formula: ||v|=  √(v1^2)+(v1^2)

So:
||v|= √(32)+(42) ||v|=  √9+16 ||v|= <span>√</span>25  ||v|= 5
8 0
3 years ago
Solve arctan(-sqrt(3))
tatyana61 [14]
We are given with the expression arctan(-sqrt(3)) and asked to evaluate it. In this case, we can use a calculator or the rule of common triangles to answer this question. the value of <span>arctan(-sqrt(3)) is -60. Since negative tan is found in 2nd and 4th quadrant, the angles are 180-60 or 120 degrees and 360-60 or 300 degrees.</span>
6 0
3 years ago
Given the following functions f(x) and g(x), solve f[g(10)] and select the correct answer below: f(x) = 10x + 8 g(x) = x + 9 2,0
ikadub [295]
ANSWER
f(g(10)) = 198

EXPLANATION

The given functions are;

f(x) = 10x + 8
and

g(x) = x + 9


To find
f(g(10))
we need to find

f(g(x)) = f(x + 9)


f(g(x)) =10(x + 9) + 8



f(g(x)) =10x + 90 + 8


f(g(x)) =10x + 98



f(g(10)) = 10(10) + 98


f(g(10)) = 100 + 98


f(g(10)) = 198


The last option is the correct answer
7 0
3 years ago
Read 2 more answers
Who did this? Tell me answers for questions
erastovalidia [21]

Answer:

<h2>There are needed 3 burgers to reach the maximum measure of happiness of 25.</h2>

Step-by-step explanation:

The given function is

h(x)=-x^{2} +6x+16

Where x is the number of burgers and h the measure of happiness.

To find the maximum burgers needed to reach the maximum happiness, we just need to find the vertex of this function, which is defined as

V(h,k) where h=-\frac{b}{2a}, and b=6, a=-1, replacing these values, we have

h=-\frac{6}{2(-1)}=3

k=f(3)=-(3)^{2} +6(3)+16=-9+18+16=25

Therefore, there are needed 3 burgers to reach the maximum measure of happiness of 25.

3 0
2 years ago
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