A community for students.
Here's the question you clicked on:
 0 viewing
whatisthequestion
 2 years ago
Find the second derivaive of y = x / (x^3 1)
whatisthequestion
 2 years ago
Find the second derivaive of y = x / (x^3 1)

This Question is Closed

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0have you tried quotient rule or product rule + chain rule?

whatisthequestion
 2 years ago
Best ResponseYou've already chosen the best response.0yes I got the first derivative correctly (verified by Wolfram Alpha) but am messing up when taking the derivative the second time

whatisthequestion
 2 years ago
Best ResponseYou've already chosen the best response.0the first derivative is \[\frac{ 2x ^{3}+1 }{ (x ^{3}1)^{2} }\]

Aperogalics
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1352709544762:dw

whatisthequestion
 2 years ago
Best ResponseYou've already chosen the best response.0I know the quotient rule and chain rule but something is wrong with my execution of the rules

Aperogalics
 2 years ago
Best ResponseYou've already chosen the best response.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:)

whatisthequestion
 2 years ago
Best ResponseYou've already chosen the best response.0I am open to other methods if you have another method let me know

Aperogalics
 2 years ago
Best ResponseYou've already chosen the best response.0first make it into an equation. can u make.......try :)

jvromero
 2 years ago
Best ResponseYou've already chosen the best response.2\[y = \frac{ x }{ x^31 } = \frac{1}{x^2\frac{1}{x}}=\left[ x^2x^{1} \right]^{1}\] \begin{align} y' &= (1)\left[ x^2x^{1} \right]^{2} (2x  (1)x^{2}) \\ &= [ x^2x^{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^56x^2)(x^3  1)^{3} + (6x^2)(x^3  1)^{2}\\ &= \frac{12x^56x^2}{(x^3  1)^3} + \frac{6x^2}{(x^3  1)^2}\\ &= \frac{12x^56x^2}{(x^3  1)^3} + \frac{(6x^2)(x^3  1)}{(x^3  1)^3}\\ &= \frac{12x^56x^2 6x^5 +6x^2}{(x^3  1)^3}\\ &= \frac{6x^5}{(x^3  1)^3}\\ \end{align}

jvromero
 2 years ago
Best ResponseYou've already chosen the best response.2verification: 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
Ask your own question
Sign UpFind 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
 Engagement 19 Mad Hatter
 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.