# Absolutely STUCK on a 2nd derivative

#### mateomy

Absolutely STUCK on a 2nd derivative!!!

1. The problem statement, all variables and given/known data

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#### mateomy

Re: Absolutely STUCK on a 2nd derivative!!!

Thanks for that. Im reading on how to use LaTeX right now. Again, thanks.

#### joeghal87

Re: Absolutely STUCK on a 2nd derivative!!!

Hello there,

here is the problem, your second derivative is wrong it should be:

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

then what you have to do is multiply by (x^2+x-2)^(1/2) both the numerator and the denominator

thus you'll obtain this form :

y" = (2(x^2+x-2)-(2x+1)^2)/(2(x^2+x-2)^(3/2))

all you have to do now is develop the numerator of this expression and you'll get this :

y" = (-2x^2-2x-5)/(2(x^2+x-2)^(3/2))

here you go, and to get the exact one like the book, u have to multiply by 2 both numerators and denominators... Your book should have done the simplification already though...

#### mateomy

Re: Absolutely STUCK on a 2nd derivative!!!

Hello there,

here is the problem, your second derivative is wrong it should be:

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

then what you have to do is multiply by (x^2+x-2)^(1/2) both the numerator and the denominator

thus you'll obtain this form :

y" = (2(x^2+x-2)-(2x+1)^2)/(2(x^2+x-2)^(3/2))

all you have to do now is develop the numerator of this expression and you'll get this :

y" = (-2x^2-2x-5)/(2(x^2+x-2)^(3/2))

here you go, and to get the exact one like the book, u have to multiply by 2 both numerators and denominators... Your book should have done the simplification already though...

Thanks, but Im still confused. Why would you want to multiply the denominator and numerator by 2? I know it will make the expression match what I have in the book, but what would be the ultimate purpose (besides and answer match) to doing the multiplication?

Super appreciative for the help, btw.

#### joeghal87

Re: Absolutely STUCK on a 2nd derivative!!!

the purpose : absolutely nothing at all :) actually your book just didn't simplify the expression to the fullest... if you divide by 2 the numerator and deminator in the final expression reached from the book, you get to the one I found... like I said, they should have done the simplification themselves :)

and you're welcome ! anytime :)

#### mateomy

Re: Absolutely STUCK on a 2nd derivative!!!

Thank you so much. I've been pacing around all morning trying to figure out why that looked the way it did.

And now...on to yet more problems.

THANKS!!

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