2010
51
22.14
54
( 2 24 2010 )
: .., ..
: ..
: . ..
= f() Δ Δ, Δ .
= f() - : y′ f′(x) , - .
,
(1)
(1) , x . . = y′(a) f′(a). f′(x) - .
s=f(t) , s , , t , v=s′=f′(x) . .
y=f′(x), x0, 0(x0,y0), , 0(x0,y0).
y′(x0)=tgφ=kkac
φ- , k .
( ) . .
, u v x, u′ v′.
:
1. (C)′=0 (C - const)
2. (x)′=1
3. y=uv, y′=u′v′
4. y= , y′=
5. y=uv, y′=u′v+uv′
6. y=f(u), u=(x) u u , .. x u .
, y′x=yu′∙ ux′
, .
|
|
()′=α∙uα-1∙u′ (1)
() ′= - ∙u′ (1)
() ′= ∙u′ (1)
() ′= ∙lna∙u′ (2)
() ′= ∙u′ (2a)
(ln u)′= ∙u′ (3)
()= ∙u′ (3a)
(sin u)′=cos u∙u′ (4)
(cos u)′=-sin u∙u′ (5)
(tg u)′ = ∙u′ (6)
(ctg u)′= - ∙u′ (7)
(arcsin u)′= ∙u′ (8)
(arccos u)′= - ∙u′ (9)
(arctg u)′= ∙u′ (10)
(arcctg u)′= - ∙u′ (11)