# [SOLVED] Find first and second derivative.

• Sep 3rd 2009, 08:50 PM
el123
[SOLVED] Find first and second derivative.
$\displaystyle f(x) = 2x^2+\frac{8}{x^2}$

$\displaystyle f'(x) = 4x +16x^{-1} => 4x+\frac{16}{x}$

$\displaystyle f''(x) = 4 -16$

Is that right?
• Sep 3rd 2009, 08:55 PM
Rapha
Hi el123!

Quote:

Originally Posted by el123
$\displaystyle f(x) = 2x^2+\frac{8}{x^2}$

$\displaystyle f'(x) = 4x +16x^{-1} => 4x+\frac{16}{x}$

No, that is not correct. You tried to integrate or something.

If
$\displaystyle g(x) := 8*\frac{1}{x^2} = 8*x^{-2}$

then

$\displaystyle g'(x) = -2*8*x^{-2-1} =-2*8*x^{-3} = -16*\frac{1}{x^3}$

Thus $\displaystyle f'(x) = 4x -16*\frac{1}{x^3}$

Do you think you find the second derivative on your own?

Yours
Rapha
• Sep 3rd 2009, 09:03 PM
el123
is it $\displaystyle f''(x) = 4 +48x^{-4}$?
• Sep 3rd 2009, 09:06 PM
Rapha
Hello.

Quote:

Originally Posted by el123
is it $\displaystyle f''(x) = 4 +48x^{-4}$?

That is correct.

$\displaystyle f''(x) = 4 +48x^{-4} = 4 + \frac{48}{x^4}$

Rapha
• Sep 3rd 2009, 09:08 PM
el123
Cheers mate.