Function Expression :
\[f(x)=-\frac{2x}{x^2+1} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} - \frac{2}{x^{2} + 1} \]\[f^{\,\prime}(x)=\frac{2 \left(x^{2} - 1\right)}{\left(x^{2} + 1\right)^{2}} \]
\[ \]
Integral
\[F(x) = - \log{\left(x^{2} + 1 \right)} \]Sign Table
Variation Table
Plot
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