limy=A, y=A+a
limDy/Dx=y`, Dy/Dx=y`+a, Dy=y`Dx+aDx
Dx0
Dy=y`Dx+e, e-...,
,, Dx(a),
.
dy=y`Dx
- . ,
..
D
- ...
, D.
y=x, dy=dx=x`Dx=Dx, dx=Dx
y¹x, dy=y`dx, y`=dy,dx
:
,
- (x0,f(x0))
x0 Dx
-:
1. (UV)`=U`V`, (UV)`dx=U`dxV`dx,
d(UV)=d(UV)
2. (UV)`=U`V+V`U, (UV)`dx=V`dU+U`dV
3.d(c)=c`dx=0*dx=0
4. d(U/V)`=(V`dU-U`dV)/V2.
.
f(x)
/ [a,b] .
(a,b) f(a)=f(b) .
. (a,b), , f(c)=0.