Differentiation 4/x^-2

**Jelley** · June 15th 2012, 07:53 AM

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

i know it basic stuff , having one of those days

**Goku** · June 15th 2012, 07:59 AM

$\frac{4}{x^{-2}} = 4x^2$

Now differentiate...

**biffboy** · June 15th 2012, 08:01 AM

x^-2=1/x^2 So 4/x^-2= 4x^2 whose derivative=8x

**HallsofIvy** · June 15th 2012, 09:36 AM

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!

**richard1234** · June 15th 2012, 12:44 PM

Quotient rule, boo...lol

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

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