对,用复合函数求导法.
y = (1+x²)/(1-x³)
= -(x³+1)(x³-1)
= -(x³-1+2)(x³-1)
= -[1 + 2/(x³-1)]
= - 1 - 2/(x³-1)
dy/dx = 0 + [2/(x³-1)^2]3x²
= 0 + 6x²/(x³-1)²
或写成:
dy/dx = 6x²/(1-x³)²
一楼的方法是对的,但是y的表达式丢了负号,结果会变成负的,那就错了.
因为求导本身会多出来一个负号,负负得正.结果是正的.
对,用复合函数求导法.
y = (1+x²)/(1-x³)
= -(x³+1)(x³-1)
= -(x³-1+2)(x³-1)
= -[1 + 2/(x³-1)]
= - 1 - 2/(x³-1)
dy/dx = 0 + [2/(x³-1)^2]3x²
= 0 + 6x²/(x³-1)²
或写成:
dy/dx = 6x²/(1-x³)²
一楼的方法是对的,但是y的表达式丢了负号,结果会变成负的,那就错了.
因为求导本身会多出来一个负号,负负得正.结果是正的.