设e^xy-xy^2=Siny,求dy/dx

题目

设e^xy-xy^2=Siny,求dy/dx

答案

你好!
两边对x求导：
e^(xy) *(y+xy') - y^2 = y' cosy
解得 y' = (y^2 - ye^(xy) ) / ( xe^(xy) - cosy )