(arctanx)' = ? (arcsinx)' = ?

(arctanx)' = ?

$$\tan{ (\arctan{(x)} ) } = x \quad | \quad \frac{d}{dx} \\\\
\left[ 1 + \tan^2{( \arctan{(x)} )} \right] \times [\arctan{(x)} ]' = 1
\right(
\\\\
\left( 1 + x^2 \right) \times [\arctan{(x)} ]' = 1
\right)\\\\
\boxed{[\arctan{(x)} ]' = \frac{1}{ 1 + x^2 }
\right)}$$

Here are the derivatives of the inverse trig functions.........http://tutorial.math.lamar.edu/Classes/CalcI/DiffInvTrigFcns.aspx

(arctanx)' = ? (arcsinx)' = ?

$$(\arcsin(x))' = \ ? \\\\
\boxed{ \sin{ ( \arcsin{(x)} ) } = x } \quad | \quad \frac {d}{dx} \\\\
cos{ ( \arcsin{(x)} ) } * (\arcsin(x))' = 1$$

$$\small{
(\arcsin(x))' =
\frac{1}
{ cos{ ( \arcsin{(x)} ) }
} \quad | \quad cos{ ( \arcsin{(x)} ) } = \sqrt{ 1- sin^2{ ( \arcsin{(x)} ) } } = \sqrt{ 1- x^2 } }
}\\\\
\boxed{(\arcsin(x))' = \frac{1}
{ \sqrt{ 1- x^2 } }}$$