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
bogdanovich [222]
3 years ago
14

If 5-y^2=x^2 then find d^2y/dx^2 at the point (2, 1) in simplest form. ​

Mathematics
1 answer:
ratelena [41]3 years ago
3 0

Answer:

y"(2, 1) = -5

Step-by-step explanation:

Step 1: Define implicit differentiation

5 - y² = x²

Step 2: Find dy/dx

  1. Take implicit differentiation: -2yy' = 2x
  2. Isolate y': y' = 2x/-2y
  3. Isolate y': y' = -x/y

Step 3: Find d²y/dx²

  1. Quotient Rule: y'' = [y(-1) - y'(-x)] / y²
  2. Substitute y': y" = [-y - (-x/y)(-x)] / y²
  3. Simplify: y" = [-y - x²/y] / y²
  4. Multiply top/bottom by y: y" = (-y² - x²) / y³
  5. Factor negative: y" = -(y² + x²) / y³

Step 4: Substitute and Evaluate

y"(2, 1) = -(1² + 2²) / 1³

y"(2, 1) = -(1 + 4) / 1

y"(2, 1) = -5/1

y"(2, 1) = -5

You might be interested in
Can someone help me with this math question & show steps ?
forsale [732]

a xuz if u work it out ull get a

7 0
4 years ago
Read 2 more answers
Without using a calculator, choose the statement that best describes the value of the square root of 86
zubka84 [21]
The value of square root 86 is between 9 and 9.5
5 0
3 years ago
What is d and how would I find its value
denis23 [38]
D-value (meteorology) in meteorology refers to the deviation of actual altitude along a constant pressure surface from the standard atmosphere altitude of that surface.
3 0
3 years ago
12x^2y-32xy+8y factored form
siniylev [52]
Factor the following:
12 x^2 y - 32 x y + 8 y
Hint: | Factor common terms out of 12 x^2 y - 32 x y + 8 y.
Factor 4 y out of 12 x^2 y - 32 x y + 8 y:
Answer:  4 y (3 x^2 - 8 x + 2)
8 0
3 years ago
Read 2 more answers
PLEASE GEOMETRY HELP WILL MARK BRAINLIEST!!!
yan [13]
D is the correct answer
7 0
3 years ago
Other questions:
  • If you know that 4 times 5 equals 20 how can you use the commutave property of multiplication to find 5 x 4
    6·1 answer
  • What is the area of the sector, in square units, determined by an arc with a measure 45° in a circle with radius 6? Round to the
    12·1 answer
  • The graph below shows three functions: Graph of function f of x equals 0.5 to the power x. Graph of function g of x is a line se
    15·2 answers
  • What do I have to do
    15·1 answer
  • What is the fifth term of the sequence defined by f(n)=3(n-3)
    12·1 answer
  • The ratio of men to women in a certain factory is 3 to 4. There are 216 men. How many workers are there ?
    8·1 answer
  • Please help me LOL I really need help
    6·2 answers
  • The scale factor of the dimensions of two similar wood floors is 4:3. It costs $207 to refinish the smaller wood floor. At that
    6·1 answer
  • Can someone please help me with math
    12·1 answer
  • What value of a make the equation 14-a=19-12
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!