1. ## Need help with this derivative please

The problem is differentiate (r^2)/(sqrt[r]+1)

I ended up with (3/2)r^(3/2)+2r in the numerator and (sqrt[r]+1)^2 in the denominator.

Is this correct so far and if so how do I simplify it more?

The answer apparently is r(4+3sqrt[r]) in the numerator and 2(1+sqrt[r])^2 in the denominator.

2. Originally Posted by kep84
The problem is differentiate (r^2)/(sqrt[r]+1)

I ended up with (3/2)r^(3/2)+2r in the numerator and (sqrt[r]+1)^2 in the denominator.

Is this correct so far and if so how do I simplify it more?

The answer apparently is r(4+3sqrt[r]) in the numerator and 2(1+sqrt[r])^2 in the denominator.
you mean $\displaystyle \frac {d}{dr} \frac {r^2}{\sqrt {r} + 1}$ ?

if so, you are correct. i wouldn't really worry about simplifying anymore. it's fine

3. yay i'm right i figured that my answer was fine, but now i am curious to see how they got to that form.

4. Originally Posted by kep84
yay i'm right i figured that my answer was fine, but now i am curious to see how they got to that form.
what form did they get it to? maybe they used the product rule and not the quotient rule

5. Originally Posted by Jhevon
what form did they get it to? maybe they used the product rule and not the quotient rule

Originally Posted by kep84
The answer apparently is r(4+3sqrt[r]) in the numerator and 2(1+sqrt[r])^2 in the denominator.
this

6. Originally Posted by kep84
this
using the product rule i get $\displaystyle \frac {4r + 3r^{3/2}}{2(\sqrt {r} + 1)^2} = \frac {r(4 + 3 \sqrt {r})}{2(\sqrt {r} + 1)^2}$ as desired

to use the product rule, you must realize that $\displaystyle \frac {r^2}{\sqrt {r} + 1} = r^2 (\sqrt {r} + 1)^{-1}$