Derivatives

FL={{{x*Cos[u]*z^2-y,x^3*u*v^6-Sin[w*t]},
{t*Tan[u*w],Exp[y]*z*u-w}},
{{y^3*v^5-t,x*Log[w]*z^4},
{x-Exp[z]*w^7,y*t^8*u*v}}}; FL//MatrixForm
Multicolumn[Table[MatrixForm[D[FL,var]]->var,
{var,{x,y,z,u,v,w}}],1]