Question

Помогите найти производную

Answer 1

Ответ:

$y = {ctg}^{2} ( {x}^{2} + {5}^{x})$

$y' = 2ctg( {x}^{2} + {5}^{x} ) \times (ctg( {x}^{2} + {5}^{x} ) )'\times ( {x}^{2} + {5}^{x} )' = \\ = 2ctg( {x}^{2} + {5}^{x} ) \times ( - \frac{1}{ \sin {}^{2} ( {x}^{2} + {5}^{x} ) }) \times (2x + ln(5) \times {5}^{x} ) = \\ = - \frac{2(2x + ln(5) \times {5}^{x})ctg( {x}^{2} + {5}^{x} )}{ \sin {}^{2} ( {x}^{2} + {5}^{x} ) }$