Question

find the derivative of r/sqr root r^2+1

Answer 1

\[\frac{ r }{ \sqrt{r^2+1} }\]

Answer 2

Hello :) I might take a while to answer. Do you still want my answer?

Answer 3

yes plz i kinda got stuck at the end and got a different answer then the back of the book

Answer 4

Well usually Textbooks are wrong :) So I'll do it and give you the answer if it's the same the Textbook is wrong because we are so smart ^.^

Answer 5

hmm yup :)

Answer 6

Are you ready for my answer?? :P

Answer 7

\[\frac{ -r^2 }{ (r^2 +1) }\] does this turn into \[(r^2 +1)^{-3/2}\]

Answer 8

yup

Answer 9

Ok this is my answer and explanation :)

Well because we are dividing we will use the quotient rule.
The quotient rule states that we take the derivative of the numerator, multiply it by the denominator minus the derivative of the denominator multiplied by the numerator all divided by the denominator squared.

So...
\[ \frac{ r }{ \sqrt{r ^{2} +1} }\]
derived would be
\[\frac{ (1)(\sqrt{r ^{2} +1}) - (\frac{ 1 }{ 2 }) (r ^{2} +1)^{\frac{ -1 }{ 2}} (2r) }{( \sqrt{r ^{2} +1})^{2}}\]

So simplifying further
\[\frac{ (r ^{2} +1)^{\frac{ 1 }{ 2 }} - r(r ^{2} + 1)^{\frac{ -1 }{ 2}}}{ (r ^{2} +1) }\]
I hope you know that when a square root is squared the answer is just the term under the square root sign.
So now we see that
\[(r ^{2}+1)^{\frac{ -1 }{ 2 }}\]
can be factored out of the numerator So it would be...
\[\frac{ (r ^{2} +1)^{\frac{ -1 }{ 2 } } [(r ^{2} +1) - r] }{ (r ^{2} +1) }\]
So now we can divide
\[\frac{ (r ^{2} +1)^{\frac{ -1 }{ 2 }} }{ (r^{2} +1) }\]
By subtracting the exponents
So we get
\[(r ^{2} +1)^{\frac{ -3 }{ 2 }} (r ^{2} - r +1)\]
So we don't like our equations with negatives so we will take it to the denominator
\[\frac{ (r ^{2} -r+1) }{ (r ^{2} +1)^{\frac{ 3 }{ 2 }} }\]

And that's the answer :) the numerator can't be factored to that's it :)

Is that what you got?

Answer 10

nope i got wat i wrote above :(

Answer 11

oh what did the textbook say?

Answer 12

\[\left( r^2+1 \right)^{-3/2}\]

Answer 13

Aww then I have no idea :P I guess this will stay a mystery. You should check with your teacher all 3 solutions and see which one is right then tell me so we can celebrate who the smartest person is :)
Sorry I was no help :(

Answer 14

yup ill ask her...we r all smart and u helped me a lot thanx :)

Answer 15

YAY thanks :)