Question

срочно! найти производную
1)y=1/4 tg^4x
2)y=arcsin 2/x
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Answer 1

Ответ:

$1)y = \frac{1}{4} {tg}^{4} x$

$y' = \frac{1}{4} \times 4 {tg}^{3} (x) \times \frac{1}{ {cos}^{2} (x)} = \frac{ {tg}^{3}( x) }{ {cos}^{2}(x) }$

$2)y = arcsin( \frac{2}{x} )$

$y' = \frac{1}{1 - \frac{4}{ {x}^{2} } } \times ( - 2 {x}^{ - 2} ) = \frac{1}{ \sqrt{1 - \frac{4}{ {x}^{2} } } } \times ( - \frac{2}{ {x}^{2} } ) = - \frac{2}{ \sqrt{ {x}^{4} (1 - \frac{4}{ {x}^{2} } )} } = - \frac{2}{ \sqrt{ {x}^{4} - 4 {x}^{2} } } = - \frac{2}{x \sqrt{ {x}^{2} - 4} }$