Question

Найти производную функции

Answer 1

Ответ:

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

$( ln(y)) ' = ( ln( {sh3x}^{arctg(x + 2)} ) ' = \\ = ((arctg(x + 2) \times (ln(sh(3x)))' = \\ = \frac{1}{1 + {(x + 2)}^{2} } \times ln(sh(3x)) + \frac{1}{sh3x} \times ch3x \times 3 \times arctg(x + 2) = \\ = \frac{ln(sh(3x))}{1 + {x}^{2} + 4 x + 4 } + 3cth(3x) \times arctg(x + 2) = \\ = \frac{ln(sh(3x))}{ {x}^{2} + 4x + 5 } + 3cth(3x)arctg( x + 2)$

$y '= {(sh3x)}^{arctg(x + 2)} \times ( \frac{ln(sh(3x))}{ {x}^{2} + 4x + 5} + 3cth(3x)arctg( x+ 2))$