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DiKsa [7]
3 years ago
6

Y=3x^2+6x-7/(x+1)^2 Show that dy/dx = 20/(x+1)^3

Mathematics
1 answer:
fredd [130]3 years ago
3 0
Apply the quotient rule  
d(uv)  =    v du/dx - u dv/dx
  dx           ----------------------
                         v^2

 du/dx  =  6x + 6
 dv/dx   =  2(x + 1)
 v^2 = (x + 1)^4   so we have

dy dx =  (x + 1)^2 .* (6x + 6) - (3x^2 + 6x - 7) * 2(x + 1)   /  (x + 1)^4

         =   (x + 1) [(6(x + 1)^2 - 2(3x^2 + 6x - 7) ]  / (x + 1)^4

         =  (x^2 + 12x +6 - 6x^2  - 12x + 14 ) / (x + 1)^3  

        =  20 / (x + 1)^3   Answer
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3. Rewrite the expression as simply as you can:<br> 3x + 11y - 2x - 4y
vfiekz [6]

Answer:

x+7y

Step-by-step explanation:

First off, lets split the question into both x and y.

3x - 2x for the x

11y - 4y for the y

You can solve both of them to get x + 7y

3x - 2x = x

11y - 4y = 7y

Then, add them back up and get x + 7y

7 0
3 years ago
Read 2 more answers
What is 5,307,288 rounded the nearest 100,000
IceJOKER [234]
That's easy it is 5,300,000 I think by the way Might be wrong I hurt my eye so yea don't say I am not good at math it is my eye hurting or it can be 5,300,288 
7 0
3 years ago
Given that 2x + 1 =5, what is the value of (x+3)^3
Alla [95]

Answer: 125

Step-by-step explanation:

First, solve for x in the first equation.

1) Subtract 1 from both sides.

2x = 4

2) Divide by 2 on both sides.

x = 2

Next, substitute the value of x into the second expression.

(2 + 3)^3

= 5^3

= 125

5 0
3 years ago
Read 2 more answers
Find the average rate of change of the function from x=1 to x=2.<br><br><br><br> f(x)=−14/x^2
Irina-Kira [14]

Answer:

The average rate of change of the function from x=1 to x=2 will be: 10.5                

Step-by-step explanation:

Given the function

f\left(x\right)=-\frac{14}{x^2}

at x₁ = 1,

f(x₁) = f(1) =  -14/(1)² = -14/1 = -14

at x₂ = 2,

f(x₂) = f(2) = -14/(2)² = -14/(4) = -3.5

Using the formula to determine the average rate of change at which the total cost increases will be:

Average rate of change = [f(x₂) - f(x₁)] / [ x₂ - x₁]

                                        = [-3.5 - (-14)] / [2 - 1]

                                        = [-3.5 + 14] / [1]

                                        = 10.5 / 1

                                        = 10.5

Therefore, the average rate of change of the function from x=1 to x=2 will be: 10.5                      

6 0
3 years ago
To check the correctness of the answer to a multiplication example, divide the
zubka84 [21]

Multiplicand is the number that gets multiplied, multiplier is the number that you are multiplying by, product is the result of mulptiplication multiplicand by multiplier.


Let a be a multiplicand, b be a multiplier and c be a product, then


a·b=c.


To check the correctness of the answer to a multiplication example, you should divide the product c by the multiplier b:


c÷b=a.


Answer: correct choice is A.

5 0
3 years ago
Read 2 more answers
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