Find the derivative of the function. y=x/sqrt(x^2+1)

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Find the derivative of the function. y=x/sqrt(x^2+1)

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use uv rule
\[y=x/\sqrt{x ^{2}+1}\]
well I understand part of it

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Other answers:

use quotient rule
U-substitution, yo. Or whatever they call it nowadays.
then gemeraal power rule
general
Oh, wait, derivative, not integral. XD
i get to this answer
y=x/sqrt(x^2+1) Use Quenient and Chain rule
Alright, product rule of x*(x^2+1)^(-1/2), (x^2+1)^(-1/2)-(1/2)x(2x)(x^2+1)^(-3/2) Yeah.
\[y'=(x ^{2}+1)^{1/2} - x ^{2}(x ^{2}+1)^{-1/2}/x ^{2}+1\]
thqats the derivative now i have to figure out how to simplify it
is the answer
oh crud made a mistake (sqrt(x^2+1)) - x(2x/2sqrt((x^(2)+1)))/(sqrt(x^2+1))^(2)
that is the answer
because the final answer in the back of the book is \[1/\sqrt{(x ^{2}+1)^{3}}\]
thats the answer the book gives me
i know my first answer is correct but not simplified
simplify
if i understood how to simplify it I wouldnt be here
lol
fair enough :) i will help or try to my battery is about to die
( (sqrt(x^2+1)) - x(2x/2sqrt((x^(2)+1))) )/(sqrt(x^2+1))^(2) = ( (sqrt(x^2+1)) - (x/sqrt(x^(2)+1)) )/ (sqrt(x^2+1))^(2) = (sqrt(x^2+1)) / (sqrt(x^2+1))^(2) - ( (x/sqrt(x^(2)+1)) / (sqrt(x^2+1))^(2) ) = 1 / (sqrt(x^2+1))^(2) - ( (x/sqrt(x^(2)+1)) / (sqrt(x^2+1))^(2) )
Truly, simplification and algebraic manipulation are the difficult parts of calculus; not the class' own namesake.
Lol, yes it is in the quotient rule, thats why i hate it. xD
somehow it simplifies to
1 / (sqrt(x^2+1))^(2) - ( (x/sqrt(x^(2)+1)) / (sqrt(x^2+1))^(2) ) = 1 / (sqrt(x^2+1))^(2) - x(sqrt(x^2+1))^(2) )/sqrt(x^(2)+1) = 1 / (sqrt(x^2+1))^(2) - x(sqrt(x^2+1))/1
1 / (sqrt(x^2+1)) - x(sqrt(x^2+1)) sorry made a mistake
\[(x ^{2}+1)^{-3/2}(x ^{2}+1)/(x^2=1)\]
/x^2+1) oops
But yeah try multiplying both the top and the bottom by the conjugate: (x(sqrt(x^2+1))^(2) + 1) but as far as I would go to simplify this would be it it ( x(sqrt(x^2+1))^(2) - 1 )/(sqrt(x^2+1))
for final answer power in denominator should be 3/2
\[(\sqrt{x ^{2}+1} - x^2/\sqrt{x^2+1})/(x^2+1)\]
\[(x^2+1-x^2)/\sqrt{x^2+1}/x^2+1\]
\[1/(x^2+1)(\sqrt{x^2+1})\]
would \[(x^2+1)(\sqrt{x^2+1})= \sqrt{(x^2+1)^3}\]
because the final answer should be 1/sqrt(x+1)^3
http://www.wolframalpha.com/input/?i=y%3Dx%2Fsqrt%28x%5E2%2B1%29+find+derivative
i understand that marina same thing i have there
(x+1)^2/3 = sqrt((x+1)^2)
^3 oops
you're right y\[(x^2+1) \sqrt{x^2+1}= (x^2+1)(x^2+1)^{1/2}= (x^2+1)^{3/2}\]
i do believe \[(x^2+1)(\sqrt{x^2+1}) = \sqrt{(x^2+1)^3}\]
ok :) then the way i did that is right
Right!

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