Fórum de Matemática
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Derive a função a seguir:
\(\frac{\sqrt{x}}{2} - \frac{2}{\sqrt{x}}\)

Gabarito:
\(\frac{t + 4}{4t\sqrt{t}}\)

\(y=\frac{\sqrt x}{2}-\frac{2}{\sqrt x}\)


\(y^{\prime}=\left( \frac{\sqrt x}{2}-\frac{2}{\sqrt x} \right)^{\prime}\)


\(y^{\prime}=\left( \frac{\sqrt x}{2} \right)^{\prime} - \left( \frac{2}{\sqrt x} \right)^{\prime}\)


\(y^{\prime}=\frac{1}{2}* \left( \sqrt x \right)^{\prime} - 2* \left( \frac{1}{\sqrt x} \right)^{\prime}\)


\(y^{\prime}=\frac{1}{2}* \frac{1}{2\sqrt{x}} - 2* \left( \frac{(1)'*\sqrt x -1*(\sqrt x)^{\prime}}{(\sqrt x)^2} \right)\)


\(y^{\prime}= \frac{1}{4\sqrt{x}} - 2* \left( \frac{-1}{ 2*x \sqrt{x}} \right)\)


\(y^{\prime}=\frac{1}{4\sqrt{x}} +\frac{1}{ x \sqrt{x}}\)


\(y^{\prime}=\frac{x+4}{4x\sqrt{x}}\)