Question

Нужно найти пройзводную
1)y=(x^3+x^-2+11)^3=?
2)y=sin(5x-3)=?​

Answer 1

1

$y = {( {x}^{3} + {x}^{ - 2} + 11) }^{3}$

$y' = 3 {( {x}^{3} + {x}^{ - 2} + 11) }^{2} \times ( {x}^{3} + {x}^{ - 2} + 11) '= \\ = 3 {( {x}^{3} + \frac{1}{ {x}^{2} } + 11)}^{2} \times (3 {x}^{2} - 2 {x}^{ - 3} ) = \\ = 3(3 {x}^{2} - \frac{2}{ {x}^{3} } ) {( {x}^{3} + \frac{1}{ {x}^{2} } + 11) }^{2}$

2

$y = \sin(5x - 3)$

$y' = \cos(5x - 3) \times (5x - 3)' = 5 \cos(5x - 3) \\$