y^3=cosx+2x^2+y^2,求dy

问题描述:

y^3=cosx+2x^2+y^2,求dy

两边对x求导得,3y^2*y'=-sinx+4x+2y*y',移项得y'=(4x-sinx)/(3y^2-2y),故dy=y'dx=[(4x-sinx)/(3y^2-2y)]dx.