( , Dx0, Du0, .. u = g(x) )
.
.
.
(lnïxï)¢= , .. .
, .
f(x).
, ,
, - , .
- .
, , , . , .
u = f(x) v = g(x) , , f(x)>0.
y = uv. , :
lny = vlnu
. .
:
:
:
.
= f(x) , x = g(y) , .
x = g(y) :
.. g¢(y) ¹ 0
.. .
. arctg.
arctg , tg, .. :
,
:
.. :
, , .
.
y = f(x) :
: , a0, D0.
: .
aDx- , f¢(x)Dx, .. f¢(x)Dx- D.
. f(x) .
dy df(x).
, dy = f¢(x)Dx
dy = f¢(x)dx.
:
.
y
f(x)
K
dy
M Dy
L
a
x x + Dx x
|
|
DMKL: KL = dy = tga×Dx = y¢×Dx
, f(x) .
.
u = f(x) v = g(x)- , , :
1) d(u v) = (u v)¢dx = u¢dx v¢dx = du dv
2) d(uv) = (uv)¢dx = (u¢v + v¢u)dx = vdu + udv
3) d(Cu) = Cdu
4)
.
.
y = f(x), x = g(t), .. - .
dy = f¢(x)g¢(t)dt = f¢(x)dx.
, dy , - , .
, - ,
dx = Dx,
t, D ¹ dx.
, dy = f¢(x)Dx .
. .
:
. .
.
.
.
.