Find y' for the following.​

Find Y' For The Following.

Answers

Answer 1

Answer:

[tex]\displaystyle y' = \frac{5x - 2xy^2}{2y(x^2 - 3y)}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Derivative Rule [Product Rule]:                                                                             [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Implicit Differentiation

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle 5x^2 - 2x^2y^2 + 4y^3 - 7 = 0[/tex]

Step 2: Differentiate

Implicit Differentiation:                                                                                 [tex]\displaystyle \frac{dy}{dx}[5x^2 - 2x^2y^2 + 4y^3 - 7] = \frac{dy}{dx}[0][/tex]Rewrite [Derivative Property - Addition/Subtraction]:                                 [tex]\displaystyle \frac{dy}{dx}[5x^2] - \frac{dy}{dx}[2x^2y^2] + \frac{dy}{dx}[4y^3] - \frac{dy}{dx}[7] = \frac{dy}{dx}[0][/tex]Rewrite [Derivative Property - Multiplied Constant]:                                   [tex]\displaystyle 5\frac{dy}{dx}[x^2] - 2\frac{dy}{dx}[x^2y^2] + 4\frac{dy}{dx}[y^3] - \frac{dy}{dx}[7] = \frac{dy}{dx}[0][/tex]Basic Power Rule [Product Rule, Chain Rule]:                                             [tex]\displaystyle 10x - 2 \Big( \frac{d}{dx}[x^2]y^2 + x^2\frac{d}{dx}[y^2] \Big) + 12y^2y' - 0 = 0[/tex]Basic Power Rule [Chain Rule]:                                                                     [tex]\displaystyle 10x - 2 \Big( 2xy^2 + x^22yy' \Big) + 12y^2y' - 0 = 0[/tex]Simplify:                                                                                                         [tex]\displaystyle 10x - 4xy^2 - 4x^2yy' + 12y^2y' = 0[/tex]Isolate y' terms:                                                                                             [tex]\displaystyle -4x^2yy' + 12y^2y' = 4xy^2 - 10x[/tex]Factor:                                                                                                           [tex]\displaystyle y'(-4x^2y + 12y^2) = 4xy^2 - 10x[/tex]Isolate y':                                                                                                       [tex]\displaystyle y' = \frac{4xy^2 - 10x}{-4x^2y + 12y^2}[/tex]Simplify:                                                                                                         [tex]\displaystyle y' = \frac{5x - 2xy^2}{2y(x^2 - 3y)}[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Book: College Calculus 10e


Related Questions

PLEASE write an equation in point-slope form for the line that passes through the point with the given slope. (-2,11) m=4/3

Answers

Answer:

[tex]y-11=\frac{4}{3}(x+2)[/tex] or y - 11 = (4/3)(x+2)

Step-by-step explanation:

Point-slope equation is:  [tex]y-y_1=m(x-x_1)[/tex]

If we replace y1 with 11 and x1 with -2 then this will be our resulting formula:

[tex]y-11=m(x+2)[/tex]

And of course we need to replace m with our slope:

[tex]y-11=\frac{4}{3}(x+2)[/tex]

What is the missing number that makes the ratios equivalent?
12:9
_:18​

Answers

Answer:

24

Step-by-step explanation:

someone said it is D CAN SOMEONE TELL ME THE RIGHT ONE

Answers

It is 1.16 ML

You welcome

2(4x - 1) < 4(3x+1), where x ∈ {set of all negative Integers}​

Answers

[tex]\large\underline{\sf{Solution-}}[/tex]

Given inequation:

[tex]\sf 2(4x-1)<4(3x+1), x\in \{Set\ of\ negative\ integers\}[/tex]

[tex]\sf\longmapsto 8x-2<12x+4[/tex]

[tex]\sf\longmapsto 8x-2-4<12x+4-4[/tex]

[tex]\sf\longmapsto 8x-6<12x[/tex]

[tex]\sf\longmapsto 8x-6-8x<12x-8x[/tex]

[tex]\sf\longmapsto -6<4x[/tex]

[tex]\sf\longmapsto 4x>-6[/tex]

[tex]\sf\longmapsto \dfrac{4x}{4}>\dfrac{-6}{4}[/tex]

[tex]\sf\longmapsto x >-1\dfrac{1}{2}[/tex]

Therefore:

[tex]\sf\longmapsto\boxed{ x=\{-1\}}\ \ Ans.[/tex]

What are all the fractions that are between 1/2 and 1.

Answers

Answer:

2/4, 3/5,3/4, 2/3,13/25, 27/50 11/20, 14/25, 29/50,31/50, 63/100,16/25,33/50,17/25,7/10,18/25,37/50,19/25,77/100,39/50,4/541/50, 83/100, 21/25 , 17/20, 43/50 , 87/100,22/25,9/10, 91/100, 23/25, 93/100, 47/50, 19/20 , 24/25  97/100, 49/50,99/100(note that I did not state all the fractions between 1/2 and 1)

Step-by-step explanation:

Firstly one half(1/2) represents 0.50 as a decimal and 1 would be 1.00

This is like saying finding Fractions that give you percentages between 50% and 100%

for example:

you could simplify 52/100 and get 31/50

31/50 as a decimal would be 0.52  and 0.52 falls between(0.50 and 1.00) 1/2 and 1

example 2: 89/100= 0.9 (same as0.90) and [90/100] is same as 9/10 = 0.9

0.90 or 0.9 (zero point nine) is not the same as 0.09(zero point zero nine

If you are using a casio calculator, you can simplify the fraction by putting in your numerator then pressing |a b/c| button then enter the denominator, then the calculator should simplify the fraction, if the fraction remains the same, this means that it cant be further simplified.if your calculator has

| a b/c| then you can also use it.

or use an online calculator or simplify if you wish

To find the decimal of that fraction you can simply divide the numerator by the denominator, Example; 82/100 is same as 0.82 and 41/50 is same as 0.82.

The diagonal of a side of rhombus are of equal length. Find the measures of angles of the rhombus.​

Answers

Explanation:

Consider ABCD is a rhombus

We know that

All sides are equal in rhombus i.e,

⇛AB=BC=CD=DA

and AC and BD are digonals

Given that

Diagonal and the side of the rhombus are equal.

⇛AB = BC = CD = DA = AC

Diagonal AC divides the rhombus into two triangles .

They are ∆ BAC and ∆ DAC

In triangle BAC

BA=BC=AC,(Given)

⇛∠ BAC=∠ABC= ∠ACB =60°→→→Eqn(i)

Similarly in ∆DAC ,

DA=DC=AC

⇛∠DAC=∠ACD=∠ADC=60°→→→Eqn(ii)

From eqn(i) and eqn(ii)

∠A=∠BAC+∠DAC=60°+60°=120°

and

∠B= ∠ABC = 60°.

and

∠C=∠ACB+∠ACD=60°+60°=120°

and

∠D =∠ADC=60°

∴ ∠A = 120° , ∠B = 60° ,∠C = 120° & ∠D = 60°

Answer:-The measures of the all angles in the rhombus are 120° , 60° ,120° and 60°.

Note: [Figure refers in the attached file.

Find the equation of the polynomial function graphed below.

A) f(x) = x3 − 3x2 − 6x + 8

B) f(x) = 8x3 − 24x2 − 48x + 64

C) f(x) = x3 + 3x2 − 6x − 8

D) f(x) = 8x3 + 24x2 − 48x − 64

Answers

Answer:

See image

Step-by-step explanation:

Check out the y-intercepts for these equations and look at the y-intercept on the graph. The y-intercept is the point where x=0. So it's mental math you can do in a couple of seconds per equation. If x=0 all the x terms are zero and the y-intercept is just the constant at the end if the equation. I put a note on the graph and the answer choices. The constant is the y-intercept. Only one choice matches. See images.

A) f(x) = x3 − 3x2 − 6x + 8

10. Andy has trumpet practice 4 times every month. Every practice lasts half an hour. What is the total number of minutes that Andy will practice?​

Answers

Answer:

480min a month

Step-by-step explanation:

4×30 =120

120×4=480

nvmnvmnvmvnmvnmvnvnmvv

Answers

Answer:

ur right

Step-by-step explanation:

Find the equation in standard form of the line passing through the points (6, 3) and (1,5)

Answers

Answer:

2x+5y=27

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(5-3)/(1-6)

m=2/-5

m=-2/5

y-y1=m(x-x1)

y-3=-2/5(x-6)

y-3=-2/5x+12/5

y=-2/5x+12/5+3

y=-2/5x+12/5+15/5

y=-2/5x+27/5

y-(-2/5x)=27/5

y+2/5x=27/5

5(y+2/5x)=5(27/5)

5y+2x=27

2x+5y=27

(x-3)^2=5 ? confused

Answers

[tex](x-3)^2=5\implies \sqrt{(x-3)^2}=\sqrt{5}\implies (x-3)=\sqrt{5}\implies x = \sqrt{5}+3[/tex]

Can someone pls help me!! And if u can explain how u do it I will very thankful for that..

Answers

Answer:

For the first question is 8y, and the second question would be 80

Step-by-step explanation:

The perimeter of a shape is calculated by adding it's sides together, and 2y+2y+2y+2y=8y. If y=10, we can substitute y for 10 in which 8*10 is 80.

A race director is preparing for an upcoming marathon and estimates that the mean time to
finish is 310 minutes. Assume
that the times are normally distributed, with a standard deviation of 50 minutes.
Use a standard normal table or a calculator to find the percentage of times that are longer than 236 minutes. For your
intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example
98.23%).

Answers

93.06% of the race is longer than 236 minutes.

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean,\sigma=standard\ deviation[/tex]

Given that μ = 310, σ = 50

For x > 236:

[tex]z=\frac{236-310}{50}=-1.48[/tex]

From the normal distribution table:

P(x > 236) = P(z > -1.48) = 1 - P(z < -1.48) = 1 - 0.0694 = 0.9306 =  93.06%

93.06% of the race is longer than 236 minutes.

Find out more on z score at: https://brainly.com/question/25638875

Identify the first five terms of the sequence in which a1 = 3 and an = 4an−1− 5 for n ≥ 2.

Answers

Step-by-step explanation:

a1 = 3

an = 4an-1 - 5

a2 = 4×3 - 5 = 12 - 5 = 7

a3 = 4×7 - 5 = 28 - 5 = 23

a4 = 4×23 - 5 = 92 - 5 = 87

a5 = 4×87 - 5 = 348 - 5 = 343

Answer:

3, 7, 23, 87, 343

Step-by-step explanation:

Using the recursive rule and a₁ = 3 , then

a₂ = 4a₁ - 5 = 4(3) - 5 = 12 - 5 = 7

a₃ = 4a₂ - 5 = 4(7) - 5 = 28 - 5 = 23

a₄ = 4a₃ - 5 = 4(23) - 5 = 92 - 5 = 87

a₅ = 4a₄ - 5 = 4(87) - 5 = 348 - 5 = 343

Nick drives 7 miles in ten minutes how many miles would nick drive if he drove at the same rate for 2 hours?

Answers

Answer 84 miles

Step-by-step explanation:

2hrs= 120min

7 miles/ 10 min = x miles/ 120 min

x = 84 miles

Answer:
84 miles
Explanation:
2 hours = 120 minutes
120 / 10 = 12
12 x 7 = 84

help please, i'm confused

Answers

Answer: C

Step-by-step explanation:

Answer huuhHH

Step-by-step explanation:

First one to put an answer gets Brainliest

What is 6-9461946105$)/&!5803&573!2.72!/‘u get Rory • 3

Answers

Answer:

I got its 69 or 六十九

Step-by-step explanation:

I need help with this

Answers

Answer:    y = (-5/4)x - 8

========================================================

Explanation:

Recall that y = mx+b is the slope intercept form of any linear equation

m = slopeb = y intercept

The given equation has m = 4/5 as the slope. Flip the fraction to get 5/4 and then flip the sign to get -5/4

The original slope is 4/5 and the perpendicular slope is -5/4. Note how the slopes multiply to -1.

The slope for the answer is -5/4 and the y intercept for the answer is -8

Therefore, the perpendicular line is y = (-5/4)x - 8

i’m 70% sure it’s y=-5/4x -8


In Manhattan, there are 15 CoffeeStops per 100,000 people Manhattan has approximately 1,602,000 people How many Coffee Stops are there?

Answers

Answer:

Given that 15coffee stops=100,000people

then: x= 1,602,000

100,000×x= 15×1,602,000

100,000x= 24,030,000

100,000x÷100,000= 24,030,000÷100,000

x= 240.3

so therefore there are 240.3 coffee stops if there are 1,602,000

Manhattan has approximately 1,602,000 people. Then the number of coffee shops will be 241.

What are ratio and proportion?

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

In Manhattan, there are 15 CoffeeStops per 100,000 people.

Then the number of coffee shops per person will be

⇒ 15 / 100,000

⇒ 1.5 × 10⁻⁴ coffee shops per person

Manhattan has approximately 1,602,000 people.

Then the number of coffee shops will be

⇒ 1,602,000 × 1.5 × 10⁻⁴

⇒240.3 or 241 coffee shops

Manhattan has approximately 1,602,000 people. Then the number of coffee shops will be 241.

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

#SPJ5

Ali caught a fish that weighed 9 1/2 lb. Lisa caught a fish that weighed 5 3/4 lb. How much more did Ali’s fish weigh?

Answers

Answer: the answer is 3 3/4

9.5-5.75=3.75. brainliest please!!!

51.33333333 just round it plz

Answers

Answer:

51

Step-by-step explanation:

The answer would be 51 because the numbers behind the decimal are below 5

Answer:

51

Step-by-step explanation:

51.33333333 rounds to 51 because 3 is less than 5.

When rounding, always look at the number before the first number in front of the decimal. If it is more than 5, round up. If it is less than, round down.

What is the equation of the line that passes through the point (8,-4) and has a slope of 1/2

Answers

Answer:

y = 1/2x - 8

Step-by-step explanation:

Assuming that they want the equation in slope intercept form we would use the following form: y = mx + b

where m = slope and b = y intercept.

We are given the slope and a point on the line. We need to find the y intercept. We can do this by plugging in what we are given and then solving for b.

y = mx + b

slope (m) = 1/2

x value of given point (x) = 8

y value of given point (y) = -4

- plug in these values -

-4 = (1/2)(8) + b

now solve for b

multiply 1/2 and 8

-4 = 4 + b

subtract 4 from both sides

-8 = b

So the y intercept (b) is -8

We now plug in the slope and y intercept into slope intercept form

y = mx + b

m = 1/2 and b = -8

y = 1/2x - 8 is the equation of the line that passes through the point (8,-4) and has a slope of 1/2

For more validation refer to the attached image.

[tex]\text{Given that,}\\\\(x_1,y_1) = (8,-4), ~~ \text{and slope, m} = \dfrac 12\\\\\text{Equation with given points,}\\\\y -y_1 = m(x-x_1)\\\\\implies y -(-4) = \dfrac 12 (x-8)\\\\\implies y+4 = \dfrac 12 x - 4\\\\\implies y= \dfrac 12x -4 -4 \\\\\implies y = \dfrac 12 x -8\\\\\implies y = \dfrac{x-16}2\\\\\implies 2y = x -16\\\\\implies x -2y = 16[/tex]

Write a number using the following clues:

a multiple of 6
• greater than 30 but less than 90

Answers

Answer: The answer is 36(multiple possible answers though).

Points M (2, 9) and N (-1, 3) are on a line with y-intercept 5. What is the equation of the line?

Answers

Answer:

Whenever you are given two points, start by naming the points.  (2, 9) becomes (x1, y1); then (-1, 3) becomes (x2, y2).  When you know which numbers you are putting into which formulas, it makes it much easier.

Start with finding your slope.  m = y2 - y1/ x2 -x1

Step-by-step explanation:

Hope This Helps! Please Mark Brainliest!

Please help thank you

Answers

Answer:

2 × n - 1 = x

Step-by-step explanation:

for example:

[tex]2(4) - 1 = 7[/tex]

[tex]2(5) - 1 = x \\ 10 - 1 = x \\ x = 9[/tex]

Help I need the answers ASAP

Answers

Answer:

7296 / 24 = 304

9216 / 18 = 512

11. 304
12. 512
those are the answers sorry if i’m late

Five and 1/3÷2 2/3 simplified

Answers

Answer:

5 1/3 ÷ 2 2/3

Write both mixed fractions (whole number in front of fully-reduced fraction) as improper fractions (numerator is larger than denominator).

5 1/3 = 16/3

2 2/3 = 8/3

16/3 ÷ 8/3

When dividing, switch the numerator and the denominator of the fraction after the division sign and change the division sign to a multiplication sign.

16/3 x 3/8

Multiply.

16/8

Divide by 8.

2

Hope this helps! :)

What is the perimeter of the trapezoid?
10m
8m
10m
18m

Answers

Answer:

  46 m

Step-by-step explanation:

The perimeter of any figure is the sum of the lengths of its sides.

  8m +10m +10m +18m = 46 m

The perimeter of the figure is 46 meters.

Help someone I don’t know the answer and I need help!

Answers

the correct answer is (-4,4) i hope this helped :)

Answer: I believe the answer is (A)  (-4,4) because the only corner that's going up towards the (f) is stopped over the 4's.

ABC has vertices A(-3,2). B(3,2), and C(0, – 3). Is ABC scalene, isosceles, or equilateral?
Is ABC scalene, isosceles, or equilateral?

Answers

Answer:

isoselses!

Step-by-step explanation:

i hope that helps

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