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anonymous
 3 years ago
Find the second derivaive of y = x / (x^3 1)
anonymous
 3 years ago
Find the second derivaive of y = x / (x^3 1)

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

anonymous
 3 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

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

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

anonymous
 3 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

anonymous
 3 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:)

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

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[y = \frac{ x }{ x^31 } = \frac{1}{x^2\frac{1}{x}}=\left[ x^2x^{1} \right]^{1}\] \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}

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0verification: 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
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