# Differentiation 4/x^-2

• June 15th 2012, 07:53 AM
Jelley
Differentiation 4/x^-2
Hey guys, having a blank moment

Could some one just give me an answer to the the derivative of 4/x^-2, the x to the power -2 has thrown me a bit , longer time since i did this (Thinking) i know it basic stuff , having one of those days
• June 15th 2012, 07:59 AM
Goku
Re: Differentiation 4/x^-2
$\frac{4}{x^{-2}} = 4x^2$

Now differentiate...
• June 15th 2012, 08:01 AM
biffboy
Re: Differentiation 4/x^-2
x^-2=1/x^2 So 4/x^-2= 4x^2 whose derivative=8x
• June 15th 2012, 09:36 AM
HallsofIvy
Re: Differentiation 4/x^-2
The hard way, using the "quotient rule": (f/g)'= (f'g- fg')/g^2 with f= 4, a constant so f'= 0, and $g= x^{-2}$ so $g'= -2x^{-3}$. $(4/x^2)'= [(0)(x^{-2})- (4)(-2x^{-3}]/x^{-4}= 8x^{-3}/x^{-4}= 8x^{-3-(-4)}= 8x$

Gosh, wasn't that fun!
• June 15th 2012, 12:44 PM
richard1234
Re: Differentiation 4/x^-2
Quotient rule, boo...lol

$\frac{d}{dx} \frac{4}{x^{-2}} = \frac{d}{dx} 4x^2 = 8x$