WZORY TRYGONOMETRYCZNE ctg x = cos x sin 2x = 2 sinxcosx

WZORY TRYGONOMETRYCZNE ctg x = cos x sin 2x = 2 sinxcosx

WZORY TRYGONOMETRYCZNE
sin x
tg x = cos
x
x
ctg x = cos
sin x
2x
sin2 x = 1−cos
2
2x
cos2 x = 1+cos
2
sin2 x + cos2 x = 1
sin 2x = 2 sin x cos x
cos 2x = cos2 x − sin2 x
ASYMPTOTY UKOŚNE
y = mx + n
m = lim
x→±∞
f (x)
,
x
n = lim [f (x) − mx]
x→±∞
POCHODNE
[f (x) + g(x)]0 = f 0 (x) + g 0 (x)
[f (x) − g(x)]0 = f 0 (x) − g 0 (x)
[cf (x)]0 = cf 0 (x), gdzie c ∈ R
0
[f (x)g(x)]
= f 0 (x)g(x) + f (x)g 0 (x)
h
i0
0
f (x)
(x)g 0 (x)
= f (x)g(x)−f
, o ile g(x) 6= 0
g(x)
g 2 (x)
0
[f (g(x))] = f 0 (g(x))g 0 (x)
[f (x)]g(x) = eg(x) ln f (x)
(c)0 = 0, gdzie c ∈ R
(xp )0 = pxp−1
√
( x)0 = 2√1 x
( x1 )0 = − x12
(ax )0 = ax ln a
(ex )0 = ex
(loga x)0 = x ln1 a
(ln x)0 = x1
(sin x)0 = cos x
(cos x)0 = − sin x
(tg x)0 = cos12 x
(ctg x)0 = − sin12 x
1
(arc sin x)0 = √1−x
2
1
(arc cos x)0 = − √1−x
2
1
(arc tg x)0 = 1+x
2
1
(arc ctg x)0 = − 1+x
2
1