Chain Rule

Total Derivative

See Total Derivative $f:{\mathbb{R}}^p\to {\mathbb{R}}^m$ and $g:{\mathbb{R}}^n\to {\mathbb{R}}^p$

$$D(f(g(x)))=Df(g(x))Dg(x)$$

1 dimensional

$$(f(g(x)){)}^{\prime }=f^{\prime }(g(x))\cdot g^{\prime }(x)$$

Flat Multidimensional

$$(f(x(a,b,c),y(a,b,c),z(a,b,c)){)}_c=f_x{x}_c+f_y{y}_c+f_z{z}_c$$