Question

найдите производную функцию 1) y=3х+2
2)y= -3/x
3) y=x²(3x+x³)
4) y=3x-2/5x+8

Помогите 60 баллов даю, напиши подробно


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Answer 1

Ответ:

$1)y = 3x + 2$

$y' = 3$

$2)y = - \frac{3}{x} = - 3 {x}^{ - 1}$

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

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

$y' = ( {x}^{2} )' \times (3x + {x}^{3}) + (3x + {x}^{3} ) '\times {x}^{2} = \\ = 2x(3x + {x}^{3} ) + (3 + 3 {x}^{2} ) \times {x}^{2} = \\ = 6 {x}^{2} + 2 {x}^{4} + 3 {x}^{2} + 3 {x}^{4} = 5 {x}^{4} + 8 {x}^{2}$

$4)y' = \frac{3x - 2}{5x + 8}$

$y = \frac{(3x - 2)'(5x + 8) - (5x + 8)'(3x - 2) }{{(5x + 8)}^{2} } = \\ = \frac{3(5x + 8) - 5(3x - 2)}{ {(5x + 8)}^{2} } = \frac{15x + 24 - 15x + 10}{ {(5x + 8)}^{2} } = \\ = \frac{34}{ {(5x + 8)}^{2} }$