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