1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
BlackZzzverrR [31]
3 years ago
11

Find y' for the following.​

Mathematics
1 answer:
Varvara68 [4.7K]3 years ago
4 0

Answer:

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

General Formulas and Concepts:

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

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

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

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

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

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

Implicit Differentiation

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle 5x^2 - 2x^2y^2 + 4y^3 - 7 = 0

<u>Step 2: Differentiate</u>

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

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

Unit: Differentiation

Book: College Calculus 10e

You might be interested in
ABCD is a rectangle. Angle D = 3x + 20 + 7x - 3x. Solve for x
Elodia [21]

Answer:

angle D equal to 3 X + 20 + 7 x minus 3 x

=90 degree equal to x minus 3 X + 20

7 X equal to 70 X equal to 10

4 0
3 years ago
Evaluate the expression.
AVprozaik [17]

Answer:

add my sc = bmic ava, no spaces

or add my discord = XoXo_ava

Step-by-step explanation:

Also have a great day and remember youre worth, dont let no boy/girl tear u down. leave them h*es aside and focus on yo self!!!

4 0
2 years ago
What is the value of the constant in the equation that relates the height and
VashaNatasha [74]

Answer:

10 over=5

i asked this quetion

7 0
2 years ago
Read 2 more answers
PLS HELP ASAP<br> is this aa,sas,ss, or neither
bagirrra123 [75]

Answer:

SAS

Step-by-step explanation:

the right angles are congruent

the pairs of sides are proportional

7 0
3 years ago
Triangle ABC was dilated by 50%. What is the relationship between AC and A'C'?
Elina [12.6K]

Answer:      

The length of segment AC is two times the length of segment A'C'

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

Let

z ----> the scale factor

A'C' ----> the length of segment A'C'

AC ----> the length of segment AC

so

z=\frac{A'C'}{AC}                        

we have that

z=50\%=50/100=\frac{1}{2} ---> the dilation is a reduction, because the scale factor is less than 1 and greater than zero

substitute

\frac{1}{2}=\frac{A'C'}{AC}                

AC=2A'C'

therefore

The length of segment AC is two times the length of segment A'C'

5 0
2 years ago
Read 2 more answers
Other questions:
  • What is the half life for the zombie population
    7·1 answer
  • 11/4 hours 19/8 hours 2.6 hours witch is closest to 2 hours?
    13·1 answer
  • A guy wire makes a 67° angle with the ground. Walking out 32 feet further from the tower, the angle of elevation to the top of t
    5·1 answer
  • Por favor ayuda casi no entiendo álgebra me pueden ayudar ¡¡¡
    14·1 answer
  • 17- (9 - 10) = (17 - 9) - 10<br><br> A. True<br><br> B. False
    10·2 answers
  • I need help finding the value of x. Please help me ?
    13·1 answer
  • Determine whether the system of linear equations has one solution infinitely many solutions or no solution explain your reasonin
    11·1 answer
  • Juan has a cellular phone that costs $12.95 per month plus 25¢ per minute for each call. Tiffany has a cellular phone that costs
    13·1 answer
  • Really Easy Points!!!<br> -<br> Define potential
    8·2 answers
  • Evaluate the function rule for the given value.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!