Math (derivative by limit process)

Find the derivative of the function by the limit process.

f(x)=1/sqrt(x)

I've worked through my problem and got f'(x) to be -1/2x but the actual answer is -1/2x^3/2? Where did the 3/2 power come from?
Any help is greatly appreciated!

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  1. f(x+h)-f(x) = 1/√(x+h) - 1/√x
    = (√x - √(x+h))/√(x(x+h))
    = (x-(x+h))/(√x(x+h))(√x+√(x+h))
    = -h/(√x(x+h))(√x+√(x+h))
    divide by h and you have

    -1/(√x(x+h))(√x+√(x+h))
    as h->0, that is
    -1/(√x^2 (2√x))
    = -1/(x*2√x)

    I suspect a √ got lost somewhere in the shuffle. Should have shown your work. I might have picked it up more easily than doing it myself...

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