f(x) f'(x) +"xa dx xa+1/(a+1) + C ;a`"-1 f(x) f'(x) +"xa dx xa+1/(a+1) + C ;a`"-1
C 0 +"1/x dx ln|x| + C
C 0 +"1/x dx ln|x| + C
xa axa-1 +"ax dx ax/lna + C ;a>0, a`"-1
xa axa-1 +"ax dx ax/lna + C ;a>0, a`"-1
ex ex +"ex dx ex + C
ex ex +"ex dx ex + C
ax axlna +"sinx dx cosx + C
ax axlna +"sinx dx cosx + C
ln|x| 1/x +"cosx dx -sinx + C
ln|x| 1/x +"cosx dx -sinx + C
log |x| 1/(xlna) +"1/sin2x dx -ctgx + C
a
log |x| 1/(xlna) +"1/sin2x dx -ctgx + C
a
sinx cosx +"1/cos2x dx tgx + C
sinx cosx +"1/cos2x dx tgx + C
cosx -sinx +"1/"(1-x2) dx arcsinx + C
cosx -sinx +"1/"(1-x2) arcsinx + C
tgx 1/cos2x +"1/(1+x2) dx arctgx + C dx
ctgx -1/sin2x +"f'/f dx= ln|f| + C ;f`"0 tgx 1/cos2x +"1/(1+x2) dx arctgx + C
arcsinx 1/"(1-x2) +"fn*f' dx= fn+1/(n+1) +C
ctgx -1/sin2x +"f'/f dx= ln|f| + C ;f`"0
arccosx -1/"(1-x2) +"f'/"f dx=2"f +C
arcsinx 1/"(1-x2) +"fn*f' dx= fn+1/(n+1) +C
arctgx 1/(1+x2) +"f'/f2 dx=-1/f +c
arccosx -1/"(1-x2) +"f'/"f dx=2"f +C
arcctgx -1/(1+x2) -sin,cos cos=t -sinxdx=dt
arctgx 1/(1+x2) +"f'/f2 dx=-1/f +c
f'(x)=lim (f(x+"x)-f(x))/"x sin,-cos sin=t cosxdx=dt
"x->0
arcctgx -1/(1+x2) -sin,cos cos=t -sinxdx=dt
(f ąg)'=f'ąg' -sin-cos tg=t x=arctg dx=1/(1+t2)dt
f'(x)=lim (f(x+"x)-f(x))/"x sin,-cos sin=t cosxdx=dt
"x->0
sin=t/"(1+t2) cos=1/"(1+t2)
(f ąg)'=f'ąg' -sin-cos tg=t x=arctg dx=1/(1+t2)dt
(f*g)'=f'g+fg' u tg(x/2)=t x/2=arctgt dx=2/(1+t2) dt
sin=t/"(1+t2) cos=1/"(1+t2)
sin=2t/(1+t2) cos=(1-t2)/(1+t2)
(f*g)'=f'g+fg' u tg(x/2)=t x/2=arctgt dx=2/(1+t2) dt
(f/g)'=(f'g-fg')/g2 +"uv' dx= uv - +"vu' dx
sin=2t/(1+t2) cos=(1-t2)/(1+t2)
(f g)=f'(g)*g'
(f/g)'=(f'g-fg')/g2 +"uv' dx= uv - +"vu' dx
fg=fg*(g'lnf+g*(f'/f)) f(x +"x)H"f(x )+f'(x )*"x
0 0 0
(f g)=f'(g)*g'
st. y=f(x) w P ( x ,y ): y-y =f'(x )(x- x ), y =f(x )
0 0 0 0 0 0 0 0
fg=fg*(g'lnf+g*(f'/f)) f(x +"x)H"f(x )+f'(x )*"x
0 0 0
no. y=f(x) w P ( x ,y ): y-y =(-1/f'(x ))(x- x ), y =f(x )
0 0 0 0 0 0 0 0
st. y=f(x) w P ( x ,y ): y-y =f'(x )(x- x ), y =f(x )
0 0 0 0 0 0 0 0
aul a=lim f(x)/x b=lim [f(x)-ax]
x-" x-"
no. y=f(x) w P ( x ,y ): y-y =(-1/f'(x ))(x- x ), y =f(x )
0 0 0 0 0 0 0 0
aup a=lim f(x)/x b=lim [f(x)-ax]
x" x"
aul a=lim f(x)/x b=lim [f(x)-ax]
x-" x-"
aup a=lim f(x)/x b=lim [f(x)-ax]
x" x"