求函数的导数f(x)=(x–1)(x-2)^2(x-3)^3求f(1)的导数
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令 f(x) = (x–1)(x-2)²(x-3)³ = y
lny = ln(x-1) + 2ln(x-2) + 3ln(x-3)
1/y * y ′ = 1/(x-1) + 2/(x-2) + 3/(x-3)
y ′ = y * {1/(x-1) + 2/(x-2) + 3/(x-3)}
= (x–1)(x-2)²(x-3)³ * {1/(x-1) + 2/(x-2) + 3/(x-3)}
= (x-2)²(x-3)³ + 2(x–1)(x-2)(x-3)³ + 3 (x–1)(x-2)²(x-3)²
f ′(1) = (1-2)²(1-3)³ + 2(1–1)(1-2)(1-3)³ + 3 (1–1)(1-2)²(1-3)²
= (-1)² * (-2)³ + 0 + 0
= - 8
lny = ln(x-1) + 2ln(x-2) + 3ln(x-3)
1/y * y ′ = 1/(x-1) + 2/(x-2) + 3/(x-3)
y ′ = y * {1/(x-1) + 2/(x-2) + 3/(x-3)}
= (x–1)(x-2)²(x-3)³ * {1/(x-1) + 2/(x-2) + 3/(x-3)}
= (x-2)²(x-3)³ + 2(x–1)(x-2)(x-3)³ + 3 (x–1)(x-2)²(x-3)²
f ′(1) = (1-2)²(1-3)³ + 2(1–1)(1-2)(1-3)³ + 3 (1–1)(1-2)²(1-3)²
= (-1)² * (-2)³ + 0 + 0
= - 8
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