First use product rule to give dxd(cos(exy)⋅yexy)=dxd(cos(exy))⋅yexy+dxd(yexy)⋅cos(exy) then differentiate implicitly. Remember that d/dx(f(y))=dxdy⋅dyd(f(y)).
Does anyone else think people often have misconceptions about differentiating and using wrong notation/not fully understanding it. Are schools to blame? Like you see dxdy(x)=1.