Question

f(x)=x(x²-1)(x²-2)求导

Answer 1

首先使用乘法法则，对于 f(x) 中的每一项进行求导：
f'(x) = [x]'(x²-1)(x²-2) + x[(x²-1)]'(x²-2) + x(x²-1)[(x²-2)]'
然后简化每一项：
f'(x) = (1)(x²-1)(x²-2) + x(2x)(x²-2) + x(x²-1)(2x)
f'(x) = (x²-1)(x²-2) + 2x³(x²-2) + 2x³(x²-1)
f'(x) = (x²-1)(x²-2+2x³+2x³-2x³)
f'(x) = (x²-1)(3x⁴-2)
因此，f(x) 的导数为 f'(x) = (x²-1)(3x⁴-2)。

Answer 2

f'(x)=(x²-1)(x²-2)*1 + x(2x)(x²-2) + x(x²-1)(2x)
=(x²-1)(x²-2) + 2x³(x²-2) + 2x³(x²-1)
=(x²-1)(x²-2) + 4x⁵ - 2x³