Question

Найти производную функции

Answer 1

Ответ:

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

$( ln(y))' = ( ln( {\arccos(3x)}^{\lg(5x - 1)} ) )' = \\ = (\lg(5x - 1) \times ln(\arccos (3x)))' = \\ = \frac{1}{ ln(10) \times (5x - 1)} \times 5 ln(\arccos(3x)) + \frac{1}{\arccos 3x} \times ( - \frac{1}{ \sqrt{1 - 9 {x}^{2} } } ) \times 3\lg(5x - 1) = \\ = \frac{5ln(\arccos3x)}{(5x - 1) ln(10) } - \frac{3\lg(5x - 1)}{ \sqrt{1 - 9 {x}^{2} } \arccos3x}$

$y' = {(\arccos3x)}^{\lg(5x - 1)} \times ( \frac{5 ln(\arccos3x) }{(5x - 1) ln(10) } - \frac{3\lg(5x - 1)}{ \sqrt{1 - 9 {x}^{2} }\arccos3x } )$