隐函数求导sin(xy)+1=x^3*y^3sin(xy)+1=x^3*y^3 不好意思是求二阶导数_数学解答

隐函数求导sin(xy)+1=x^3*y^3
sin(xy)+1=x^3*y^3
不好意思是求二阶导数

人气：461 ℃　时间：2019-12-28 02:43:30

解答

[sin(xy)]'
=cos(xy)*(xy)'
=cos(xy)*(y+x*y')
=ycos(xy)+xcos(xy)*y'
(xy)³=3(xy)²*(xy)'
=3(xy)²(y+x*y')
=3y(xy)²+3x(xy)²*y'
所以ycos(xy)+xcos(xy)*y'=3y(xy)²+3x(xy)²*y'
y'=[ycos(xy)-3y(xy)²]/[3x(xy)²-xcos(xy)]