Question

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

Answer 1

use uv rule

Answer 2

\[y=x/\sqrt{x ^{2}+1}\]

Answer 3

well I understand part of it

Answer 4

use quotient rule

Answer 5

U-substitution, yo. Or whatever they call it nowadays.

Answer 6

then gemeraal power rule

Answer 7

general

Answer 8

Oh, wait, derivative, not integral. XD

Answer 9

i get to this answer

Answer 10

y=x/sqrt(x^2+1)
Use Quenient and Chain rule

Answer 11

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.

Answer 12

\[y'=(x ^{2}+1)^{1/2} - x ^{2}(x ^{2}+1)^{-1/2}/x ^{2}+1\]

Answer 13

thqats the derivative now i have to figure out how to simplify it

Answer 14

is the answer

Answer 15

oh crud made a mistake
(sqrt(x^2+1)) - x(2x/2sqrt((x^(2)+1)))/(sqrt(x^2+1))^(2)

Answer 16

that is the answer

Answer 17

because the final answer in the back of the book is \[1/\sqrt{(x ^{2}+1)^{3}}\]

Answer 18

thats the answer the book gives me

Answer 19

i know my first answer is correct but not simplified

Answer 20

simplify

Answer 21

if i understood how to simplify it I wouldnt be here

Answer 22

lol

Answer 23

fair enough :) i will help or try to my battery is about to die

Answer 24

( (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) )

Answer 25

Truly, simplification and algebraic manipulation are the difficult parts of calculus; not the class' own namesake.

Answer 26

Lol, yes it is in the quotient rule, thats why i hate it. xD

Answer 27

somehow it simplifies to

Answer 28

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

Answer 29

1 / (sqrt(x^2+1)) - x(sqrt(x^2+1))
sorry made a mistake

Answer 30

\[(x ^{2}+1)^{-3/2}(x ^{2}+1)/(x^2=1)\]

Answer 31

/x^2+1) oops

Answer 32

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))

Answer 33

for final answer power in denominator should be 3/2

Answer 34

\[(\sqrt{x ^{2}+1} - x^2/\sqrt{x^2+1})/(x^2+1)\]

Answer 35

\[(x^2+1-x^2)/\sqrt{x^2+1}/x^2+1\]

Answer 36

\[1/(x^2+1)(\sqrt{x^2+1})\]

Answer 37

would \[(x^2+1)(\sqrt{x^2+1})= \sqrt{(x^2+1)^3}\]

Answer 38

because the final answer should be 1/sqrt(x+1)^3

Answer 39

http://www.wolframalpha.com/input/?i=y%3Dx%2Fsqrt%28x%5E2%2B1%29+find+derivative

Answer 40

i understand that marina same thing i have there

Answer 41

(x+1)^2/3 = sqrt((x+1)^2)

Answer 42

^3 oops

Answer 43

you're right
y\[(x^2+1) \sqrt{x^2+1}= (x^2+1)(x^2+1)^{1/2}= (x^2+1)^{3/2}\]

Answer 44

i do believe \[(x^2+1)(\sqrt{x^2+1}) = \sqrt{(x^2+1)^3}\]

Answer 45

ok :) then the way i did that is right

Answer 46

Right!