differentitation超急!!!

x³ - 3x²y + 3xy² - y³ = 8

(d/dx)(x³ - 3x²y + 3xy² - y³) = (d/dx)(8)

(d/dx)x³ - (d/dx)3x²y + (d/dx)3xy² - (d/dx)y³ = 0

(d/dx)x³ - 3x²(d/dx)y - 3y(d/dx)x² + 3x(dy/dx)y² + 3y²(d/dx)x - (d/dx)y³ = 0

3x² - 3x²(dy/dx) - 6xy + 6xy(dy/dx) + 3y² - 3y²(dy/dx) = 0

3x²(dy/dx) - 6xy(dy/dx) + 3y²(dy/dx) = 3x² - 6xy + 3y²

(3x² - 6xy + 3y²)(dy/dx) = 3x² - 6xy + 3y²

dy/dx = 1

x^3 - (3x^2) y + 3x(y^2) - y^3 = 8

3x^2 - [6xy + (3x^2) (dy/dx)] + 3(y^2) + 6xy (dy/dx)
- 3y^2 (dy/dx) = 0

3x^2 - 6xy - (3x^2) (dy/dx) + 3(y^2) + 6xy (dy/dx)
- 3y^2 (dy/dx) = 0

3x^2 - 6xy + 3(y^2) = [3x^2 - 6xy + 3y^2] (dy/dx)

x^2 - 2xy + y^2 = (x^2 - 2xy + y^2) (dy/dx)

(dy/dx) = 1


2010-10-14 22:46:46 補充：
請投我一票...