Derivata

Derivata di espressione trigonometrica

$\displaystyle y = \tan ^2 \sqrt{x}$

$\displaystyle y' = 2 \tan \sqrt{x} \cdot D \left( \tan { \sqrt{ x } } \right) =$

$\displaystyle = 2 \tan \sqrt{x} \cdot \left( 1 + \tan ^2 { \sqrt{ x } } \right) \cdot D \left( \sqrt{ x } \right) =$

$\displaystyle = 2 \tan \sqrt{x} \cdot \left( 1 + \tan ^2 { \sqrt{ x } } \right) \cdot \left( { 1 \over 2 } { 1 \over { \sqrt{ x } } } \right) =$

$\displaystyle = { { \tan \sqrt{x} + \tan ^2 { \sqrt{ x } } } \over { \sqrt{ x } } }$