1. ## Derivative Problem

Find the derivate of the following algebraic function:
$\displaystyle f(x) = (x^3 + 3x + 2) / (x^2 - 1)$

I think I am supposed to use the quotient rule, but I can't seem to get the algebra to work. My calculator says the derivative at, say, 1 is 300,000, and I get far less than that. I'm wondering if I am entering it incorrectly in my calculator or just not solving it right as it doesn't seem very simplified when I get through with it.

2. Originally Posted by seuzy13
Find the derivate of the following algebraic function:
$\displaystyle f(x) = (x^3 + 3x + 2) / (x^2 - 1)$

I think I am supposed to use the quotient rule, but I can't seem to get the algebra to work. My calculator says the derivative at, say, 1 is 300,000, and I get far less than that. I'm wondering if I am entering it incorrectly in my calculator or just not solving it right as it doesn't seem very simplified when I get through with it.
$\displaystyle f(x)=\frac{x^3+3x+2}{x^2-1}$

$\displaystyle f'(x)=\frac{(x^2-1)(3x^2+3)-(x^3+3x+2)(2x)}{(x^2-1)^2}$

You can't evaluate the derivative at 1 because the denominator is 0 when x=1

3. You mean you can't simplify it any further than that? I'm not necessarily concerned with the derivative at 1, I was just checking it as an example to see if it I was working it out right. Appears I should have chosen a different number. Anyway, I'm trying to find the derivate with respect to x not the derivative at 1.

4. Sure you can simplify more, I was just showing you what direct use of the quotient rule gives you

$\displaystyle f'(x)=\frac{(x^2-1)(3x^2+3)-(x^3+3x+2)(2x)}{(x^2-1)^2}$

$\displaystyle =\frac{3x^4+3x^2-3x^2-3-(2x^4+6x^2+4x)}{(x^2-1)^2}$

$\displaystyle =\frac{x^4-6x^2-4x-3}{(x^2-1)^2}$

5. I see now. I was making a simple multiplication mistake. It's funny how you can make the same silly mistake no matter how many times you try to do the problem. The answer still seems complicated, but I guess that's as far as it goes.
Thank you!