POCHODNE

Wzór funkcji y = /(jc)	Pochodna /'(jc) funkcji/	Uwagi
f(x) = c	(c) = 0	CG R
f(x) = ax + b	(ax + b) —a
f(x) = ax^2 +bx + c	(ax^2 +bx + c) =2 ax + b
f(x) = x“	(x^a)' = a • x^a~^l	cce /?\{0,1}
f(x) = yfx	W - 2>x	jc > 0
/(■*)=- X	f a \ -a X X^2V / ^A	jc * 0
f(x) = Vx	(v*)= „r7T'^neWU0,i} n ■ V jc"^-1	jc > 0
f(x) = sinx	(sinjc) = cosjc
/(jc) = cosjc	(cos x) = -sin jc
f(x)=tgx	(tg*) = 2 COS X	n . jc * — + kn 2 dla keC
f(x) = ctgx	(ctg*) - . 2 sin ~ x	x^kn dla keC
f(x) = a^x	(a')' = a“ ■ Ina	a> 0
f(x)=e*	(4=*‘
f{x) = \nx	(lnjc/ = — X	jc > 0
/(*)= \n\x\	(^|nN)^,=7	jc^O
f(x) = \ogax	^('°^S°^x)=xlna	a > 0, a * 1 jc>0
/(Jt) = arc sin x	(arc sin x)' = . ^ VI-jc^2	W<!
f (x) = arc cos x	(arc cosjc/ = ,—^ VI - jc^2	jc| < 1
f(x) = arctgx	(arc tg*) = 1 + jr
/(*) = arc ctg*	(arc ctg*) = l + jr