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f(x) = [itex]ln(x)/\sqrt{x}[/itex]

For f'(x), I used the quotient rule and received f'(x) = (([itex]\frac{1}{x}[/itex][itex]\sqrt{x}[/itex])-([itex]\frac{-\sqrt{x}}{2}[/itex]ln(x))) / 2

However, I plugged f(x) into wolfram alpha and it gave me: [itex]\frac{2-ln(x)}{2x^{3/2}}[/itex]

I don't understand the difference? I thought I had done this correctly but apparently not? Wolfram alpha used the product rule. Is there some kind of algebraic gymnastics I'm forgetting about? I really want to understand where my error was made, not just which is the correct answer. Thanks!