Найти производную сложной функции : y = (cos2x) ^arctg√x

Найти производную сложной функции : y = (cos2x) ^arctg√x

ln (y) = ln ((cos2x) ^arctg√x)

(1/y) ·y ⁽¹⁾ =[ln ((cos2x) ^arctg√x) ] ⁽¹⁾

y ⁽¹⁾ =y·[ (arctg√x) ·ln (cos2x) ] ⁽¹⁾

y ⁽¹⁾ =[ (cos2x) ^arctg√x]·[{ (arctg√x) } ⁽¹⁾ ·ln (cos2x) + (arctg√x) ·{ln (cos2x) } ⁽¹⁾ ]

y ⁽¹⁾ =[ (cos2x) ^arctg√x]·

·[{1 / (1+x) }· (1 / (2√x)) ·ln (cos2x) + (arctg√x) ·{1 / (cos2x) }· (-sin2x) ·2]=

=[ (cos2x) ^arctg√x]·{ln (cos2x) / (2 (√x) (x+1)) - 2· (sin2x) · (arctg√x) / cos2x}