In neural computing, a neural response $($y$)$ is obtained by multiplying the input signal $($vector x$)$ with a weight matrix

$($W$),$ offset by a vector b as follows.

$1$

y $=$ Wx $+$ b$,(6)$

where W is an m by d matrix, x is a d$-$dimensional vector, and the dimension of y is m similar to the dimension of

b$.$ Equation $6$ obtains a linear mapping between input x and output y$.$ To introduce non$-$linearity in this mapping

$($Equation $9),$ a Sigmoid function $\backslash$sigma $($x$)$ is used, which is defined as below.

$\backslash$sigma $($x$)=$

$1$

$1+$ e$$x $(7)$

d $\backslash$sigma $($x$)$

dx

$=\backslash$sigma $($x$)(1\backslash$sigma $($x$))(8)$

y $=\backslash$sigma $($Wx $+$ b$)(9)$

You must provide complete code with proper comments and printed results.

$$ Plot the sigmoid function for values of x ranging from $-10$ to $+10$

$$ Plot the derivative of the sigmoid function for values of x ranging from $-10$ to $+10$

$$ Plot to compare Equation $(6)$ and Equation $(9)$ where y is a function of x$.$ You may assume other values and

variables.Use python to do the question.