Question

найти производную функции
$y=\frac{sinx}{x} +\frac{x}{cosx}$

Answer 1

$y = \frac{ \sin(x) }{x} + \frac{x}{ \cos(x) } \\ y' = \frac{( \sin(x))' \times x - x' \times \sin(x) }{x {}^{2} } + \frac{x' \times \cos(x) - ( \cos(x) )' \times x}{ \cos {}^{2} (x) } = \\ = \frac{ \cos(x) \times x - \sin(x) }{x {}^{2} } + \frac{ \cos(x) - ( - \sin(x) ) \times x}{ \cos {}^{2} (x) } = \\ = \frac{x \cos(x) - \sin(x) }{ {x}^{2} } + \frac{ \cos(x) + x \sin(x) }{ \cos {}^{2} (x) }$