Question

Найти производную от сложной функции
pamagite plz

Answer 1

Ответ:

$y = ( {5}^{ - \frac{1}{x} } )'arcsin {(2x + 1)}^{3} + ( arcsin {(2x + 1)}^{3} )' \times {5}^{ - \frac{1}{x} } = \\ = ln(5) \times {5}^{ - \frac{1}{x} } \times ( - {x}^{ - 1} )'arcsin {(2x + 1)}^{3} + \frac{1}{ \sqrt{1 - {(2x + 1)}^{6} } } \times ( {(2x + 1)}^{3} ) '\times (2x + 1)' \times {5}^{ - \frac{1}{x} } = \\ = {5}^{ - \frac{1}{x} } ( ln(5) \times {x}^{ - 2} \times arcsin {(2x + 1)}^{3} + \frac{3 {(2x + 1)}^{2} \times 2}{ \sqrt{1 - {(2x + 1)}^{6} } } ) = \\ = {5}^{ - \frac{1}{x} } ( \frac{ ln(5) \times arcsin {(2x + 1)}^{3} }{ {x}^{2} } + \frac{6 {(2x + 1)}^{2} }{ \sqrt{1 - {(2x + 1)}^{6} } } )$