# Derivative of 1/x^2

• 09-14-2006, 06:09 PM
DrKickflip13
Derivative of 1/x^2
I'm stuck on this for homework...I dont know why its so damn hard. I did all the problems fine except for this one that I got to and then I got stuck...

Finding the derivative of 1/X^2 (we only learned the "limitation method")

I got it down to some mess of numbers like

2xh + h^2 / x^4 + 2x^3h + x^2h / h

Anyway if you have no clue what I'm taking about then nvm but its 12th grade calc homework lol :D
• 09-14-2006, 06:12 PM
Hooger
if i could read that font i might be able to help... but that font is very hard to read...
• 09-14-2006, 06:15 PM
El Diablo
• 09-14-2006, 06:17 PM
DrKickflip13
Quote:

Originally Posted by Hooger
if i could read that font i might be able to help... but that font is very hard to read...

Sorry, I forgot I was messing around and changed it to Impact. I thought it didn't work but I guess only premium members can see it. Can you read it now?
And I'm 99% sure the answer is NOT 5....
• 09-14-2006, 06:18 PM
El Diablo
i am .01% sure the answer is 5....
• 09-14-2006, 06:28 PM
DrKickflip13
lol

now I'm 99% sure the answer is... -(2/x^3)
• 09-14-2006, 06:30 PM
Hooger
na he is right i got 1(6-1) = 5.
• 09-14-2006, 08:09 PM
FreePlay
Hooger, be silent. There's no given value for x. DrKickflip13 is correct: -2/(x^3).

1/(x^2) = x^(-2). Multiply by the power, reduce the power by 1: -2*x^(-3), or -2/(x^3).
• 09-14-2006, 08:34 PM
DrKickflip13
Quote:

Originally Posted by FreePlay
Hooger, be silent. There's no given value for x. DrKickflip13 is correct: -2/(x^3).

1/(x^2) = x^(-2). Multiply by the power, reduce the power by 1: -2*x^(-3), or -2/(x^3).

Thanks a lot :D
Can you explain the shortcut you use? I used The Quotient Rule which took a while...thanks!
• 09-15-2006, 07:18 AM
FreePlay
Yep! For anything that's just a power of x times a constant, you can just multiply the constant by the power, then multiply THAT by x to the power minus one.

Example: 2x/3
Constant: 2/3
Power: 1
Derivative 2/3 * 1 * x ^ (1-1) or 2/3

Example: 17/(3*x^9)
Constant: 17/3
Power: -9
Derivative: 17/3 * -9 * x ^ (-9-1)
=51 * x ^ -10 = 51/(x^10)

Example: 32x^3
Constant: 32
Power: 3
Derivative: 32 * 3 * x ^ (3-1)
= 96x^2

If there are multiple pieces of the expression with X in them, you can just do the derivative of the pieces. Example:

8x^3 + x^2 + 2x
Constants: 8, 1, 2
Powers: 3, 2, 1
Derivative: 8*3*x^(3-1) + 1*2*x^(2-1) + 2*x^(1-1)
=24x^2 + 2x + 2

Of course, derivatives aren't always simple... once you get into the derivatives of the trig functions, it'll be more confusing.
• 09-15-2006, 04:14 PM
cowsruledaworld
Quote:

Originally Posted by DrKickflip13
I'm stuck on this for homework...I dont know why its so damn hard. I did all the problems fine except for this one that I got to and then I got stuck...

Finding the derivative of 1/X^2 (we only learned the "limitation method")

I got it down to some mess of numbers like

2xh + h^2 / x^4 + 2x^3h + x^2h / h

Anyway if you have no clue what I'm taking about then nvm but its 12th grade calc homework lol :D

im in calc and we haven't done derivatives.. we are only on limits... so sorry i cant help you there... all i know is the formula for derivatives. But i think you might be complicating the problem too much.. if you have only learned the limitation method..then there should be an easier way... its math afterall.