Question

Найдите производную функции, пожалуйста:
1) (5x-4)^6
2) 4/(3x-1)^2
3) 1/(4-3x)^5
4)cos^2x
5)sin^4x
6)e^-4x
7)In(-2x)

Answer 1

Ответ:

$1)y' = 6 {(5x - 4)}^{5} \times 5 = 30 {(5x - 4)}^{5}$

$2)y' = 4 \times ( - 2) {(3x - 1)}^{ - 3} \times 3 = \\ = - \frac{24}{ {(3x - 1)}^{3} }$

$3)y' = 1 \times ( - 5) {(4 - 3x)}^{ - 6} \times ( - 3) = \\ = \frac{15}{ {(4 - 3x)}^{6} }$

$4)y' = - 2 \sin(2x)$

$5)y'=4 { \sin }^{3} (x) \times \cos(x)$

$6)y' = - 4 {e}^{ - 4x}$

$7)y' = \frac{1}{ - 2x} \times ( - 2) = \frac{1}{x}$