Question

надо найти производную
помогите,плиз
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Answer 1

Ответ:

$y = {(\sh(3x))}^{arctg(x + 2)}$

$y' = ( ln(y))' \times y$

$( ln(y)) ' = ( ln(\sh(3x) {}^{arctg(x + 2)} )' = \\ = (arctg(x + 2) \times ln(\sh(3x)))' = \\ = \frac{1}{1 + {(x + 2)}^{2} } \times ln(\sh(3x)) + \frac{1}{\sh(3x)} \times \ch(3x) \times 3 \times arctg(x + 2) = \\ = \frac{ ln(\sh(3x)) }{1 + {x}^{2} + 4x + 4} + 3arctg(x + 2) \times \cth(3x)$

$y' = {(sh(3x))}^{arctg(x + 2)} \times ( \frac{ ln(\sh(3x))) }{ {x}^{2} + 4x + 5 } + 3arctg(x + 2) \times \cth(3x))$

Answer 2

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