.
, . (I)
.
.
(II)
1.
( )
3. ( )
4. ( )
, (III)
( )
()
()
()
(IY)
. ( )
. (Y)
.
(YI)
.
.
.
, . (I)
.
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| Y'(x) Y(x). , . Y'(x) ( ), - | |
| Y' = Lim (ΔY / ΔX), Δ X . .. | |
| " " ( Y=x2) | |
| 充. | |
| (U + V) ' = U' + V'; (U - V)' = U' - V'; (U * V)' = U' * V + U * V'; (U / V)' = (U' * V - U * V') / V 2. | |
| dY = Y * Δx = Y *dx. | |
| , . | |
| : Y' = Y'U(x) * U'x. Y'U(x) - , U'x .. | |
| : Y(Xo + ΔX) ≈ Y(Xo) + Y'(Xo) * ΔX. , . | |
| , . , : I = U / R. ( I = I(U,R)) U = U(X,Y,Z). , U - X,Y,Z. | |
| , . "x", - y z ! , U = x + xy2 - xyz4. U'x = 1 + y2 - yz4, U'y = 0 + x(2y) - xz4, U'z = xy4z3 | |
| , , : dUx = U'x * Δ x. ( ) : dU = dUx + dUy + dUz. | |
| . U. , U. . X, U. | |
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, y = Sin(x) Y' = Cos(x), - .
,
() .
, F(x) f(x),
F ' (x) = f(x).
f(x) .
∫ f(x)dx = F(x) + C
.
.
, , (3)' = 3x2,
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∫ 3x2dx = x3 + C ∫ x2dx = x3 / 3 + C.
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, . : ∫ Sin4x* Cosx*dx. , Sin4x - . :
1.
Z = Sinx.
2.
dZ = Z' * dx = Cosx * dx,
3.
dx = dZ/Cosx,
4. :
∫ z4* Cosx*dz/Cosx.
Cosx - ,
∫ z4* dz = z5/5 +C.
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∫bf(x)dx = Lim{Σ f(d)*dx} n → ∞.
- f(x) ab.
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