Given that $f:L(V,W) \times L(U,V) \to L(U,W)$ where $L(V,W)$ are the linear transformation from vector space $V$ to vector space $W$ ,given that $f(A,b) = A B$, prove that $f$ is differential and compute $Df$ ?
$f(A+G,B+H) = (A+G)(B+H) = A B +A H + G B + G H = f(A,B) + A H+ G B + G H$
i think that $AH + GB$ is the differential or because $G H$ is not linear but not quite sure, any help is appreciated.