Given the following inputs, X$,$ and corresponding desired outputs, D:

X $=\{0\mathrm{.}5,0\mathrm{.}2,0\mathrm{.}1,0\mathrm{.}3,0\mathrm{.}4,0\mathrm{.}5,0\mathrm{.}7\}$ D $=\{1,1,2,3\mathrm{.}2,3\mathrm{.}5,5,6\}$

$1.$ Let the cost function be defined as follows:

E$=1$ X$($di$$wxi$)2(1)$

$2$N i

Define an expression for the cost function with respect to w$,$ after substituting values for the input and desired output. Compute the gradient at the point w $=2$ using direct differentia$-$ tion.