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Derivative of 1/x^2

This is a discussion on Derivative of 1/x^2 within the General Off Topic+ forums, part of the QJ.net Forum Miscellaneous category; I'm stuck on this for homework...I dont know why its so damn hard. I did all the problems fine except ...

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1. 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

2. if i could read that font i might be able to help... but that font is very hard to read...

4. 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....

5. i am .01% sure the answer is 5....

6. lol

now I'm 99% sure the answer is... -(2/x^3)

7. na he is right i got 1(6-1) = 5.

8. 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).

9. 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
Can you explain the shortcut you use? I used The Quotient Rule which took a while...thanks!

10. 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.

11. 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
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.

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