Question

Нужно решить 3 примера под цифрой 2, плез:)

Answer 1

Ответ:

1)

$y = {tg}^{2} (3 {x}^{2} ) \times {e}^{2x + 2}$

$y' = 2tg(3 {x}^{2} ) \times \frac{1}{ { (\cos(3 {x}^{2} )) }^{2} } \times 6x \times {e}^{2x + 2} + 2 {e}^{2x + 2} \times {tg}^{2} (3 {x}^{2} ) = \\ {e}^{2x + 2} tg(3 {x}^{2} )( \frac{12x}{ {cos}^{2} (3 {x}^{2}) } + 2tg(3 {x}^{2} ))$

2)

$y = \cos( {x}^{5} ) \times {tg}^{2} (3 {x}^{3} + 5)$

$y' = - \sin( {x}^{5} ) \times 5 {x}^{4} \times {tg}^{2} (3 {x}^{3} + 5) + 2tg(3 {x}^{3} + 5) \times \frac{1}{ {cos}^{2} (3 {x}^{3} + 5)} \times 9 {x}^{2} \times \cos( {x}^{5} ) = \\ tg(3 {x}^{3} + 5) \times ( \frac{18 {x}^{2} \cos( {x}^{5} ) }{ {cos}^{2} (3 {x}^{3} + 5)} - 5 {x}^{4} \sin( {x}^{5} ) tg(3 {x}^{3} + 5))$

3)

$y = \sqrt[4]{1 + {cos}^{2} ( {x}^{2}) }$

$y' = \frac{1}{4} {(1 + {cos}^{2}( {x}^{2} )) }^{ - \frac{3}{4} } \times 2 \cos( {x}^{2} ) \times ( - \sin( {x}^{2}) ) \times 2x = - \frac{x \sin( {x}^{2} ) \cos( {x}^{2} ) }{ \sqrt[4]{ {(1 + {cos}^{2} ( {x}^{2} ))}^{3} } }$