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
SashulF [63]
2 years ago
13

If -y-2x^3=Y^2 then find D^2y/dx^2 at the point (-1,-2) in simplest form

Mathematics
1 answer:
algol132 years ago
6 0

Answer:

\frac{d^2y}{dx^2} = \frac{-4}{3}

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Algebra I</u>

  • Factoring

<u>Calculus</u>

Implicit Differentiation

The derivative of a constant is equal to 0

Basic Power Rule:

  • f(x) = cxⁿ
  • f’(x) = c·nxⁿ⁻¹

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

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

Quotient Rule: \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}

Step-by-step explanation:

<u>Step 1: Define</u>

-y - 2x³ = y²

Rate of change of tangent line at point (-1, -2)

<u>Step 2: Differentiate Pt. 1</u>

<em>Find 1st Derivative</em>

  1. Implicit Differentiation [Basic Power Rule]:                                                  -y'-6x^2=2yy'
  2. [Algebra] Isolate <em>y'</em> terms:                                                                              -6x^2=2yy'+y'
  3. [Algebra] Factor <em>y'</em>:                                                                                       -6x^2=y'(2y+1)
  4. [Algebra] Isolate <em>y'</em>:                                                                                         \frac{-6x^2}{(2y+1)}=y'
  5. [Algebra] Rewrite:                                                                                           y' = \frac{-6x^2}{(2y+1)}

<u>Step 3: Differentiate Pt. 2</u>

<em>Find 2nd Derivative</em>

  1. Differentiate [Quotient Rule/Basic Power Rule]:                                          y'' = \frac{-12x(2y+1)+6x^2(2y')}{(2y+1)^2}
  2. [Derivative] Simplify:                                                                                       y'' = \frac{-24xy-12x+12x^2y'}{(2y+1)^2}
  3. [Derivative] Back-Substitute <em>y'</em>:                                                                     y'' = \frac{-24xy-12x+12x^2(\frac{-6x^2}{2y+1} )}{(2y+1)^2}
  4. [Derivative] Simplify:                                                                                      y'' = \frac{-24xy-12x-\frac{72x^4}{2y+1} }{(2y+1)^2}

<u>Step 4: Find Slope at Given Point</u>

  1. [Algebra] Substitute in <em>x</em> and <em>y</em>:                                                                     y''(-1,-2) = \frac{-24(-1)(-2)-12(-1)-\frac{72(-1)^4}{2(-2)+1} }{(2(-2)+1)^2}
  2. [Pre-Algebra] Exponents:                                                                                      y''(-1,-2) = \frac{-24(-1)(-2)-12(-1)-\frac{72(1)}{2(-2)+1} }{(2(-2)+1)^2}
  3. [Pre-Algebra] Multiply:                                                                                   y''(-1,-2) = \frac{-48+12-\frac{72}{-4+1} }{(-4+1)^2}
  4. [Pre-Algebra] Add:                                                                                         y''(-1,-2) = \frac{-36-\frac{72}{-3} }{(-3)^2}
  5. [Pre-Algebra] Exponents:                                                                               y''(-1,-2) = \frac{-36-\frac{72}{-3} }{9}
  6. [Pre-Algebra] Divide:                                                                                      y''(-1,-2) = \frac{-36+24 }{9}
  7. [Pre-Algebra] Add:                                                                                          y''(-1,-2) = \frac{-12}{9}
  8. [Pre-Algebra] Simplify:                                                                                    y''(-1,-2) = \frac{-4}{3}
You might be interested in
How are rational expressions related to rational numbers?
Sholpan [36]
A rational expression is the same way that any integer is also a rational number. You can stick to any polynomial in the numerator of a fraction and put "1" in the denominator.
4 0
3 years ago
Make L the subject of the formula T=2π√L\G​
Trava [24]

Answer:

T^2=4π^2*L/G

L=(T^2*G)/4π^2

Step-by-step explanation:

hope this helps

4 0
3 years ago
Read 2 more answers
22 6/11 times 1 1/2 = ?? <br> Please help me!
Step2247 [10]
9/11 is the answer because 1 and 1/2 x 6 is 9
3 0
3 years ago
Read 2 more answers
The ratio of boys to girls on rowans swim team is 2:3.if there are 40 total swimmers on the team,how many of them are girls?
Bogdan [553]

Answer:

The ratio of girls is 24.

Step-by-step explanation:

If the total amount of swimmers is 40, you can divide it by 8 to get 5 multiples.   If three of those 5's belong to the ratio of girls, the equation is 3 x 8. The answer is 24.

6 0
3 years ago
Need help ASAP AND SHOW WORK PLEASE !! 40 points
Vinvika [58]
Area = 20
perimeter = 21

5 0
3 years ago
Read 2 more answers
Other questions:
  • The radius AND height of a cone are each doubled. What is the new volume?
    12·1 answer
  • Uus uiu angles
    13·1 answer
  • I need help with my ADD and subtraction fraction ​
    13·1 answer
  • Solve math problem for v. V-6=8
    14·2 answers
  • Simplify
    5·2 answers
  • I need this ASAP. Pls help
    13·1 answer
  • Can 10, 11, 2 be measures of the sides of a triangle
    11·1 answer
  • Nalini is a real estate agent. She is paid
    6·1 answer
  • What is the percent of change from 400,000 to 700,000?
    8·2 answers
  • Select all equations for which the point (2,3) is on the graph of the equation.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!