Question

Найти производные функции:
1)y = 6x^7
2)y = 5x+ 12
3)y = x^-9(в -9 степени) – 4x -8
4)y = 6ctgx

Answer 1

1)

$y = 6x^7$

$y' = (6x^7)'=7*6x^6=42x^6$

2)

$y = 5x+ 12$

$y'= (5x+ 12)'=(5x)'+(12)'=5+0=5$

3)

$y = x^{-9}- 4x -8$

$y'=(x^{-9}- 4x -8)'=( x^{-9})'- (4x)' -8'=-9*x^{-10}-4-0=-9x^{-10}-4$

4)

$y = 6ctgx$

$y'=(6ctgx)'=6*(-\frac{1}{sin^2x} )=-\frac{6}{sin^2x}$