[ 數學 ]dy/dx f.5

1. √y – y5 = (x – 3)7
y1/2 – y5 = (x – 3)7
(1/2)y-1/2(dy/dx) – 5y4(dy/dx) = 7(x - 3)6
(dy/dx)(1 – 10y1/2y4)/(2y1/2) = 7(x – 3)6
dy/dx = 14y1/2(x – 3)6 / (1 – 10y9/2)

2. y = (x3 – 1)2(x – 2)3
dy/dx = 2(x3 – 1)(3x2)(x – 2)3 + (x3 – 1)2(3)(x – 2)2
dy/dx = (x3 – 1)(x – 2)2[2(3x2)(x – 2) + (x3 – 1)(3)]
dy/dx = (x3 – 1)(x – 2)2(6x3 – 12x2 + 3x3 – 3)
dy/dx = 3(x3 – 1)(x – 2)2(3x3 – 4x2 – 1)