# Second Derivative

• Oct 8th 2006, 09:10 AM
c_323_h
Second Derivative
Find the second derivative:

\$\displaystyle f(x)=x/(x^2+1)\$

Thanks guys
• Oct 8th 2006, 09:54 AM
CaptainBlack
Quote:

Originally Posted by c_323_h
Find the second derivative:

\$\displaystyle f(x)=x/(x^2+1)\$

Thanks guys

I expect you are meant to use the quotient rule to do this, but since
I don't lnow it I will use the product rule:

df/dx= 1/(x^2+1) + x (-1)(2x)/(x^2+1)^2 = (x^2+1-2x^2)/(x^2+1)^2

.............= (1-x^2)/(x^2+1)^2

so:

d^2f/dx^2 = -2x/(x^2+1)^2 + (1-x^2) (-2) (2x)/(x^2+1)^3

..............= [-2x(x^2+1)=4x+4x^3]/(x^2+1)^3

..............= [2x(x^2=3)]/(x^2+1)^3

RonL
• Oct 8th 2006, 10:07 AM
c_323_h
thanks. i liked the old MHF better. what happened to latex:(
• Oct 8th 2006, 10:41 AM
topsquark
Quote:

Originally Posted by c_323_h
thanks. i liked the old MHF better. what happened to latex:(

Oh it's the same forum. LaTeX wasn't part of the last update and they are working on it. They're evidently having some sort of problem with it. It'll be back at some point and then the glory will return. :)

-Dan