Let $E(x)=L(f(g(x)))+h(x)$ where $g$:$R^d{R}^m,f$:$R^m{R}^k,L$:$R^{k}R,h$:$R^{d}R,$ and $xin{R}^d.$

Write down the gradient of $E$ with respect to $x$ as a product of intermediate gradients using chain rule. Do not skip intermediate functions.

Write the dimensionality of all the factors used in the gradient expression above.