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# Find the derivative of f(x) = (1 + 5x2)(x − x2) in two ways. use the product rule. f '(x) = perform the multiplication first. f '(x) = do your answers agree? yes no

2 months ago

## Solution 1

Guest #10154
2 months ago

Answer:

The answers agree.

Step-by-step explanation:

The product rule is:

In this problem, we have that:

So

.

Multiplication first:

## Solution 2

Guest #10155
2 months ago
The product rule states that given a function:
f(x)=g(x)h(x)
f'(x)=g'(x)h(x)+h'(x)g(x)
thus the derivative of the expression will be given by:
f(x) = (1 + 5x2)(x − x2)
g(x)=(1+5x^2)
g'(x)=10x

h(x)=(x-x^2)
h'(x)=1-2x
thus:
f'(x)=10x(x-x^2)+(1-2x)(1+5x^2)
simplifying this we get:
f'(x)=-20x^3+15x^2-12x+1

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thus
A=30000(1+2/100)^1
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A=$30600 Thus amount after 1 year was$30600
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We can suppose the equation of the plane is in the form ...
ax +by +cz = 1
By using the given point coordinates for x, y, and z, we end up with three equations in 3 unknowns. These can be described by the augmented matrix ...

Putting this in reduced row-echelon form, we find
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In a family with 8 ​children, excluding multiple​ births, what is the probability of having 7 boys and 1​ girl, in any​ order? assume that a boy is as likely as a girl at each birth
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There is a 7/8 chance there will be boys and a 1/8 chance there will be a girl

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For the particular problem raised in the introduction, assume that the total bill is $44. to answer the question "how should the bill be split?" we will create a linear equation. the unknown is how much money a single person (besides anika) must pay, so call that x. although four people (you plus three friends) went to dinner, only three are paying the unknown amount x for a total of 3x. since anika is paying$2, the total amount paid is 3x+2 dollars, which must equal the amount of the bill, $44. thus, the equation to find x is 3x+2=44. the steps for solving a linear equation are as follows: move all of the constants to the right side. move all of the variable terms (terms containing x) to the left side. divide both sides by the coefficient of the variable to isolate the variable. you will go through these steps one at a time to solve the equation and determine how much each person should pay. Solution 1 3x+2=44 3x+2(-2)=44-2 3x=42 3x/3=42/3 x=14 So each person would have to pay$14, except Anika
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A pair of two distinct dice are rolled six times. suppose none of the ordered pairs of values (1, 5), (2, 6), (3, 4), (5, 5), (5, 3), (6, 1), (6, 2) occur. what is the probability that all six values on the first die and all six values on the second die occur once in the six rolls of the two dice?
Solution 1

The probability that all six values on the first die and all six values on the second die occur once in the six rolls of the two dice is 1/6.

### What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

A pair of two distinct dice are rolled six times. suppose none of the ordered pairs of values (1, 5), (2, 6), (3, 4), (5, 5), (5, 3), (6, 1), (6, 2) occur.

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The probability that all six values on the first die and all six values on the second die occur once in the six rolls of the two dice:

P = 6/36 = 1/6

Thus, the probability that all six values on the first die and all six values on the second die occur once in the six rolls of the two dice is 1/6.

Learn more about the probability here:

brainly.com/question/11234923

#SPJ2

Solution 2
But them in order of add them all up i guess
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If the numerator of a fraction is increased by 3, the fraction becomes 3/4. If the denominator is decreased by 7, the fraction becomes 1. Determine the original fraction. Which of the following equations represents "If the numerator of a fraction is increased by 3, the fraction becomes 3/4"?
Solution 1
For this case, the original fraction is:
x / y
Where,
x = numerator
y = denominator:
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x = 9
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Answer:

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9/16
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A jar contains 8 large red​ marbles, 5 small red​ marbles, 7 large blue​ marbles, and 4 small blue marbles. if a marble is chosen at​ random, which of the conditional probabilities is​ larger, ​p(red​|large​) or ​p(large​|red​)?
Solution 1
8 large red, 5 small red, 7 large blue, 4 small blue:

totally =  24 marbles

P(red)= 13/24

let A red and B large

P(A/B)= P(A∩B)/P(B)

P(B)= 15/24 =.625

P(A∩B)= 8/24 = .333

P(A/B) =.333/.625 =.533

P(B/A) =.625/.333= 1.875

so the probability of p(large/red) is larger.

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Solution 1

Answer:

Step-by-step explanation:

Let

Differentiate partially with respect to u, v.

To find f, put in xyz.

So,

Integrate with respect to u.

Integrate with respect to v.

Solution 2
Let's capture the parameterization of the surface by the vector function

Then the surface element is given by

So the surface integral is equivalent to

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