Question

Используя схему вычесления производной, найдите производной функции:
а) y=x^2(x+2)
б) y=3x(4x-3)^-6
в) y=1/4x^4-4x

Answer 1

Ответ:

а)

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

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

б)

$y = 3x {(4x - 3)}^{ - 6}$

$y '= (3x)' {(4x - 3)}^{ - 6} + ( {(4x - 3)}^{ - 6} )' \times (4x - 3)' \times 3x = \\ = 3 {(4x - 3)}^{ - 6} - 6 {(4x - 3)}^{ - 7} \times 4 \times 3x = \\ = \frac{3}{ {(4x - 3)}^{6} } - \frac{72x}{ {(4x - 3)}^{7} }$

в)

$y = \frac{1}{4 {x}^{4} } - 4x$

$y '= (\frac{1}{4} {x}^{ - 4} )' - 4 = \frac{1}{4} \times ( - 4) {x}^{ - 5} - 4 = \\ = - \frac{1}{ {x}^{5} } - 4$