C-const, (c) '=0 математика

y=f (x) y=f’ (x) y=f (x) y=f’ (x) y = c

(c - const) y’ = 0y = ln xy’ = 1/x y = xy’ = 1y = sin xy’ = cos x y = x2 y’ = 2xy = cos xy’ = - sin x y = xn

(n принадлежит N) y’ = nxn-1 y = tg x y’ = 1 / (cos2x) y = x-n

(n принадлежит N) y’ = - nxn-1 y = ctg x y’ = - 1 / (sin2x) y = xα

(α > 0) y’ = αxα-1 y = arcsin x y’ = 1/√1 - x2 y = x-α

(α > 0) y’ = - αx-α-1 y = arccos x y’ = - 1/√1 - x2 y = ax

(a > 0, a ≠ 1) y’ = axln a y = arctg x y’ = 1 / (1 + x2) y = ex y’ = ex y = arcctg x y’ = - 1 / (1 + x2) y = logax

(a > 0, a ≠ 1) y’ = 1 / (x lna)