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Find a formula for the derivative of a given function

Find a formula for the derivative of the function

    \[ f(x) = \frac{x}{1+\sqrt{x}}, \qquad x > 0. \]


Using the formula for the derivative of a rational power of x and the quotient rule, we have

    \begin{align*}   f'(x) &= \frac{1+\sqrt{x} - x\left(\frac{1}{2}x^{-\frac{1}{2}}\right)}{(1+\sqrt{x})^2}\\[8pt]  &= \frac{2+\sqrt{x}}{2(1+\sqrt{x})^2}. \end{align*}

for x > 0.

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