Quotient Rule with radical denominator

[studentmomma]

Hello...

I cannot for the life of me figure this out I was hoping to get some help. I know what the answer is I just don't know how to get there!

g(s)=(s^2-2s+5)/(square root of s)

Ans=(3s^2-2s-5)/(2s^2/3)

Anyone out there able to help me?

 

[Ishuda]

Hello...

I cannot for the life of me figure this out I was hoping to get some help. I know what the answer is I just don't know how to get there!

g(s)=(s^2-2s+5)/(square root of s)

Ans=(3s^2-2s-5)/(2s^2/3) <===TYPO /(2s^(3/2))

Anyone out there able to help me?

There are several ways to go about it but if you want to use the quotient rule
\(\displaystyle \frac{(s^{\frac{1}{2}}) (s^2\, -\, 2s\, +\, 5)'\, -\, (s^{\frac{1}{2}})' (s^2\, -\, 2s\, +\, 5)}{s}\)
=\(\displaystyle \frac{s^{\frac{1}{2}} (2s\, -\, 2)\, -\, \frac{1}{2}s^{-\frac{1}{2}} (s^2\, -\, 2s\, +\, 5)}{s}\)

Now multiply numerator and denominator by \(\displaystyle 2s^{\frac{1}{2}}\) and simplify