ChrisV
Find the derivative of the function.
y=x/sqrt(x^2+1)
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nanda082
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use uv rule
ChrisV
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\[y=x/\sqrt{x ^{2}+1}\]
ChrisV
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well I understand part of it
ChrisV
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use quotient rule
badreferences
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U-substitution, yo. Or whatever they call it nowadays.
ChrisV
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then gemeraal power rule
ChrisV
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general
badreferences
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Oh, wait, derivative, not integral. XD
ChrisV
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i get to this answer
cuddlepony
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y=x/sqrt(x^2+1)
Use Quenient and Chain rule
badreferences
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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.
ChrisV
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\[y'=(x ^{2}+1)^{1/2} - x ^{2}(x ^{2}+1)^{-1/2}/x ^{2}+1\]
ChrisV
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thqats the derivative now i have to figure out how to simplify it
cuddlepony
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is the answer
cuddlepony
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oh crud made a mistake
(sqrt(x^2+1)) - x(2x/2sqrt((x^(2)+1)))/(sqrt(x^2+1))^(2)
cuddlepony
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that is the answer
ChrisV
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because the final answer in the back of the book is \[1/\sqrt{(x ^{2}+1)^{3}}\]
ChrisV
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thats the answer the book gives me
ChrisV
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i know my first answer is correct but not simplified
cuddlepony
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simplify
ChrisV
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if i understood how to simplify it I wouldnt be here
ChrisV
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lol
cuddlepony
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fair enough :) i will help or try to my battery is about to die
cuddlepony
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( (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) )
badreferences
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Truly, simplification and algebraic manipulation are the difficult parts of calculus; not the class' own namesake.
Mimi_x3
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Lol, yes it is in the quotient rule, thats why i hate it. xD
ChrisV
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somehow it simplifies to
cuddlepony
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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
cuddlepony
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1 / (sqrt(x^2+1)) - x(sqrt(x^2+1))
sorry made a mistake
ChrisV
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\[(x ^{2}+1)^{-3/2}(x ^{2}+1)/(x^2=1)\]
ChrisV
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/x^2+1) oops
cuddlepony
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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))
MarinaDL
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for final answer power in denominator should be 3/2
ChrisV
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\[(\sqrt{x ^{2}+1} - x^2/\sqrt{x^2+1})/(x^2+1)\]
ChrisV
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\[(x^2+1-x^2)/\sqrt{x^2+1}/x^2+1\]
ChrisV
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\[1/(x^2+1)(\sqrt{x^2+1})\]
ChrisV
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would \[(x^2+1)(\sqrt{x^2+1})= \sqrt{(x^2+1)^3}\]
ChrisV
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because the final answer should be 1/sqrt(x+1)^3
ChrisV
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i understand that marina same thing i have there
ChrisV
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(x+1)^2/3 = sqrt((x+1)^2)
ChrisV
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^3 oops
Diyadiya
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you're right
y\[(x^2+1) \sqrt{x^2+1}= (x^2+1)(x^2+1)^{1/2}= (x^2+1)^{3/2}\]
ChrisV
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i do believe \[(x^2+1)(\sqrt{x^2+1}) = \sqrt{(x^2+1)^3}\]
ChrisV
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ok :) then the way i did that is right
Diyadiya
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Right!