MATEMATYKA 2(1)

WZORY RACHUNKU RÓŻNICZKOWEGO

[f(x)+g(x|]'=f'(x)+g'(x|	[sinx]'= cosx
[cf(x|]'= cf'{x|	[cosx]^/=-sinx
[f(x|-g(x|]'=f'(x)g(x)+f(x)g'(x) rf(x|l' f'(x|g(x|-f(x)g'|x) I9MJ " [g(x|]^2	ttgx]'= —= l+tg^2x cos^2x [ctgxl'= --7-r— =-(l+ctg^2x) sm^zx
[g (f(x))]' = g'(f(x)) f '(x) ['■'(Ytl =f,(fi(yl) gdy Pochodna funkcji danej parametrycznie x = f(t) , y = g(t) dy	[arcsin x]' = ^1 -[arc cos x]'= - ^1 ^Iorctgxl'^=^ ^[arcc,9x]'=-^
dY = dt = l!!! gdy^O dx dx f'(t) ^My dt *	[ •**]'= e^x
dt	[a^x] = a^xlna
	[ lnx ] = j
tc ]'= 0 [x"]^/= nx^11*^1 txl'=l
fj-l'=_-n_ [±1'=_JL Lx"J x^n+1 L*J X^2
	[x^x] = x^x(lnx+l)
[V7]'=-J= IV7]'=-L nVx^ 2^* [^]	rin(x+Vx^2+a^2)r=--- [ln(x+Vx^2-a^2‘|]'= ' ■■