Question

решить производительные функции!

Answer 1

1.

$y = 5 \sqrt[4]{ {x}^{5} } - {x}^{5} + 6x - 1 \\$

$y' = 5 \times \frac{5}{4} {x}^{ \frac{1}{4} } - 5 {x}^{4} + 6 = \\ = \frac{25}{4} \sqrt[4]{x} - 5 {x}^{4}$

2.

$y = (1 + tg \sqrt[3]{2x + 1} )x$

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

3.

$arctgy + y = x + 2$

$\frac{1}{1 + {y}^{2} } \times y' + y' = 1 \\ y'( \frac{1}{1 + {y}^{2} } + 1) = 1 \\ y' = \frac{1}{1 + \frac{1}{1 + {y}^{2} } } \\ y' = \frac{1 + {y}^{2} }{1 + {y}^{2} + 1 } \\ y' = \frac{ {y}^{2} + 1 }{ {y}^{2} + 2}$