求导y=(1+x^3)/(1-x^3)

2个回答

  • 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.