「1」petua hasil darab [product rule]
Jika [If] y = uv
(dy/dx) = u(dv/dx) + v(du/dx)
or
f '(x) = u(dv/dx) + v(du/dx)
.
「2」petua hasil bahagi [quotient rule]
Jika [If] y = u/v
(dy/dx) = [v(du/dx) - u(dv/dx)] / v2
or
f '(x) = [v(du/dx) - u(dv/dx)] / v2
y = √x (9x-2)5
.
let u = √x , v = (9x-2)5
(du/dx) = 1/(2√x) , (dv/dx) = 45(9x-2)4
.
(note: anxn-1)
√x = x1/2
= (1/2) x(1/2)-1
= (1/2) x-(1/2)
= 1/(2√x)
.
(dy/dx) = nab(bx+c)n-1
= (9x-2)5
= 5(9x-2)5-1 (9)
= 5(9x-2)4 (9)
= 45(9x-2)4
f '(x) = u(dv/dx) + v(du/dx)
= √x [45(9x-2)4] + (9x-2)5 (1/[2√x])
= 45√x (9x-2)4 + (9x-2)5 (1/2√x)
= (9x-2)4 (45√x + (9x-2)(1/2√x)
= (9x-2)4 (45√x + [(9x-2)/(2√x)]
= (9x-2)4 (90x+9x-2 / 2√x)
= (9x-2)4 (99x-2 / 2√x) [答案]
(√x)(45) = 45√x
抽(9x-2)
example : x + 2xy = x(1+2y)
(9x-2)乘上去
变分数 [note: (45√x)(2√x) = 90x]
以上我自己的算法
