Function Expression :
\[f(x)=(x-2\sqrt{x} )e^{\sqrt{x}} \]Domain
\[\left[0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = 0 \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\left(1 - \frac{1}{\sqrt{x}}\right) e^{\sqrt{x}} + \frac{\left(\left(-1\right) 2 \sqrt{x} + x\right) e^{\sqrt{x}}}{2 \sqrt{x}} \]\[f^{\,\prime}(x)=\frac{\left(x - 2\right) e^{\sqrt{x}}}{2 \sqrt{x}} \]
\[ \]
Integral
\[F(x) = 2 x^{\frac{3}{2}} e^{\sqrt{x}} + 20 \sqrt{x} e^{\sqrt{x}} - 10 x e^{\sqrt{x}} - 20 e^{\sqrt{x}} \]Sign Table
Variation Table
Plot
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