Question

Найдите производные dy/dx заданных функций

Answer 1

1.

$y = \cos( {2}^{x} )$

$y' = - \sin( {2}^{x} ) \times ( {2}^{ {x}^{} } ) '= - \sin( {2}^{x} ) \times ln(2) \times {2}^{x} \\$

2.

$y = \frac{1 - {x}^{3} }{ \sqrt{ \pi} x} = \frac{1}{ \sqrt{\pi} } \times \frac{1 - {x}^{3} }{x} \\$

$y '= \frac{1}{ \sqrt{\pi} } \times \frac{(1 - {x}^{3}) '\times x - (x) '\times (1 - {x}^{3} )}{ {x}^{2} } = \\ = \frac{ - 3 {x}^{2} \times x - (1 - {x}^{3}) }{ \sqrt{\pi} {x}^{2} } = \frac{ - 3 {x}^{3} - 1 + {x}^{3} }{ \sqrt{ \pi} {x}^{2} } = \\ = - \frac{1 + 2 {x}^{3} }{ \sqrt{ \pi } {x}^{2} }$