Arctan Türevi (Arctanx Türevi)

Arctanx Türevi Nedir?

$y=arctanx\Rightarrow y^{\prime }=\frac{1}{1+x^2}$

Arctanx Türevi İspatı

$y=arctanx\Rightarrow x=tany$

$x^{\prime }=(tany{)}^{\prime }$

$1=y^{\prime }.(1+ta{n}^{2}y)$

$y^{\prime }.(1+ta{n}^{2}y)=1$

$y^{\prime }=\frac{1}{1+ta{n}^{2}y}$

$y^{\prime }=\frac{1}{1+x^2}$

$\ddot{O}nemli:$

$y=arctanu\Rightarrow y^{\prime }=\frac{u^{\prime }}{1+u^2}$