Here,
#1=x/y^3-ye^(x-y)#
#=>y^3=x-y^4e^(x-y)#
Diff.w.r.t. #x#, #"using "color(blue) "product and chain rule"#
#3y^2(dy)/(dx)=1-[y^4d/(dx)(e^(x-y))+e^(x-y)d/(dx)(y^4)]#
#3y^2(dy)/(dx)=1-[y^4e^(x-y)(1-(dy)/(dx))+e^(x-y)4y^3(dy)/(dx)]#
#3y^2(dy)/(dx)=1-y^4e^(x-y)+y^4e^(x-y)(dy)/(dx)-4e^(x-
y)y^3(dy)/(dx)#
#3y^2(dy)/(dx)-y^4e^(x-y)(dy)/(dx)+4e^(x-y)y^3(dy)/(dx)=1-
y^4e^(x-y)#
#(dy)/(dx)[3y^2-y^4e^(x-y)+4e^(x-y)y^3]=1-y^4e^(x-y)#
#(dy)/(dx)=(1-y^4e^(x-y))/[3y^2-y^4e^(x-y)+4e^(x-y)y^3]#