Question

Знайти похідну функції.

Answer 1

а)

$y = {x}^{3} - \frac{ {x}^{2} }{2} - \frac{5}{x} - 3 \cos(4) \\ y' = 3 {x}^{3 - 1} - \frac{2 {x}^{2 - 1} }{2} -5 {x}^{ - 1 - 1} \times ( - 1) = \\ 3 {x}^{2} - x + 5 {x}^{ - 2} = 3 {x}^{2} - x + \frac{5}{ {x}^{2} } = \\ \frac{3 {x}^{4} - {x}^{3} + 5 }{ {x}^{2} }$

б)

$y = \frac{ \sin(x) }{ {x}^{6} } \\ y' = \frac{( \sin(x))' {x}^{6} - (x {}^{6})' \sin(x) }{( {x}^{6} ) {}^{2} } = \\ \frac{ {x}^{6} \cos(x) - 6 {x}^{5} \sin(x) }{ {x}^{12} } = \\ \frac{ {x}^{5}(x \cos(x) - 6 \sin(x) ) }{ {x}^{12} } = \\ \frac{x \cos(x) - 6 \sin(x) }{ {x}^{7} }$