Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

whatisthequestion

  • 2 years ago

Find the second derivaive of y = x / (x^3 -1)

  • This Question is Closed
  1. lgbasallote
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    have you tried quotient rule or product rule + chain rule?

  2. whatisthequestion
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes I got the first derivative correctly (verified by Wolfram Alpha) but am messing up when taking the derivative the second time

  3. whatisthequestion
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the first derivative is \[-\frac{ 2x ^{3}+1 }{ (x ^{3}-1)^{2} }\]

  4. Aperogalics
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1352709544762:dw|

  5. whatisthequestion
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I know the quotient rule and chain rule but something is wrong with my execution of the rules

  6. Aperogalics
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @whatisthequestion let me tell you a good one method. which is much better than this. Do you want to know??????? or want to try with method actually there is just calculation mistakes only:)

  7. whatisthequestion
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I am open to other methods if you have another method let me know

  8. Aperogalics
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    first make it into an equation. can u make.......try :)

  9. jvromero
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[y = \frac{ x }{ x^3-1 } = \frac{1}{x^2-\frac{1}{x}}=\left[ x^2-x^{-1} \right]^{-1}\] \begin{align} y' &= (-1)\left[ x^2-x^{-1} \right]^{-2} (2x - (-1)x^{-2}) \\ &= -[ x^2-x^{-1} ]^{-2} (2x + x^{-2}) \\ &= \frac{-2x+x^{-2}}{(x^2 - x^{-1})^2}\\ &= \frac{-2x^3+1}{x^2(x^2 - x^{-1})^2}\\ &= \frac{-2x^3+1}{(x(x^2 - x^{-1}))^2}\\ &= \frac{-2x^3+1}{(x^3 - 1)^2}\\ \end{align} \begin{align} y'' &= \frac{d}{dx}[\frac{-2x^3+1}{(x^3 - 1)^2}]\\ &=\frac{d}{dx}[(x^3 - 1)^{-2}(-2x^3+1)]\\ &=\frac{d}{dx}[(x^3 - 1)^{-2}](-2x^3+1) + (x^3 - 1)^{-2} \frac{d}{dx}[(-2x^3+1)]\\ &= -2(3x^2)(x^3 - 1)^{-3}(-2x^3+1) + (x^3 - 1)^{-2} (-6x^2)\\ &= (-6x^2)(-2x^3+1)(x^3 - 1)^{-3} + (-6x^2)(x^3 - 1)^{-2}\\ &= (12x^5-6x^2)(x^3 - 1)^{-3} + (-6x^2)(x^3 - 1)^{-2}\\ &= \frac{12x^5-6x^2}{(x^3 - 1)^3} + \frac{-6x^2}{(x^3 - 1)^2}\\ &= \frac{12x^5-6x^2}{(x^3 - 1)^3} + \frac{(-6x^2)(x^3 - 1)}{(x^3 - 1)^3}\\ &= \frac{12x^5-6x^2 -6x^5 +6x^2}{(x^3 - 1)^3}\\ &= \frac{6x^5}{(x^3 - 1)^3}\\ \end{align}

  10. jvromero
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    verification: https://www.wolframalpha.com/input/?i=differentiate+%28%E2%88%922x^3%2B1%29\%28x^3%E2%88%921%29^2+with+respect+to+x

  11. Not the answer you are looking for?
    Search for more explanations.

    Search OpenStudy
    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.