Derivative of VECTOR inside summation

112 Views Asked by At

Given a two row vectors $X(n)=[x(n)\quad x(n-1)\quad... \quad x(n-N)]^T$ and $S=[S_0\quad S_1\quad ...\quad S_N]^T$ and two scalars : $a(n)$ and $b(n)$

if $$y(n)=a(n)\tanh[b(n)\sum_{i=0}^N S_i x(n-i)]$$

what is $$\frac{d(y(n))}{dS}?$$