y=f(x)y=f’(x)y=f(x)y=f’(x)y = c
(c – const)y’ = 0y = ln xy’ = 1/xy = xy’ = 1y = sin xy’ = cos xy = x2y’ = 2xy = cos xy’ = – sin xy = xn
(n принадлежит N)y’ = nxn–1y = tg xy’ = 1/(cos2x)y = x–n
(n принадлежит N)y’ = – nxn–1y = ctg xy’ = – 1/(sin2x)y = xα
(α > 0)y’ = αxα–1y = arcsin xy’ = 1/√1 – x2y = x–α
(α > 0)y’ = –αx–α–1y = arccos xy’ = – 1/√1 – x2y = ax
(a > 0, a ≠ 1)y’ = axln ay = arctg xy’ = 1/( 1 + x2 )y = exy’ = exy = arcctg xy’ = – 1/( 1 + x2 )y = logax
(a > 0, a ≠ 1)y’ = 1/(x lna)