tentukan turunan pertama dari

[tex]f(x) = \frac{ \sqrt{x} - 2 }{x} + \frac{x}{ \sqrt{x - 2} } \\ = \frac{d( {x}^{ ( - \frac{1}{2}) } - 2 {x}^{ (- 1)}) }{dx} + \frac{d(\frac{x}{ \sqrt{x - 2} })}{dx} \\ = ( - \frac{1}{2} {x}^{ (- \frac{3}{2}) } + 2 {x}^{( - 2)} ) + \frac{U'V - V'U}{ {V}^{2} } \\ \\ U = x \\
U' = 1 \\
V = \sqrt{x - 2} = {(x - 2)}^{ (\frac{1}{2}) } \\
V' = \frac{1}{2} {(x - 2)}^{ (- \frac{1}{2} )} \\ \\ = ( - \frac{1}{2} {x}^{ (- \frac{3}{2}) } + 2 {x}^{( - 2)} ) + \frac{{(x - 2)}^{ (\frac{1}{2}) } - x\frac{1}{2} {(x - 2)}^{ (- \frac{1}{2} )}}{( {{(x - 2)}^{ (\frac{1}{2}) })}^{2} } \\ = - \frac{1}{2} {x}^{ (- \frac{3}{2}) } + 2 {x}^{( - 2)} + {(x - 2)}^{ (- \frac{1}{2} )} - \frac{1}{2} x {(x - 2)}^{( - \frac{3}{2} )}
[/tex]