2y=-1+xy3(y的三次方),对x求导,答案是2y'=y的三次方+3x乘以y的2次方乘以y' 求解释,谢谢_数学解答

2y=-1+xy3(y的三次方),对x求导,答案是2y'=y的三次方+3x乘以y的2次方乘以y' 求解释,谢谢

人气：450 ℃　时间：2020-03-23 06:05:37

解答

两边分别求导,得
(2y)'=(-1+xy^3)'
2y'=(xy^3)'
2y'=x'y^3+x(y^3)' (uv)'=u'v+uv'
2y'=y^3+x*3y^2*y'
2y'=y^3+3xy^2*y'