A single perceptron with activation function f$($x$)=1-e^{(-x)}$ has been trained for binary classification into class labels $0$ and $1,$ through minimization of the squared error loss function. After the training, the values of the connection weight and bias parameters are W $=1$ and b$=-1.$ What will be the updated value of w after one more step of steepest descent with the input value x $=2$ and class label y $=0,$ if the learning rate is $1?$ Select the correct option $($a$)$ to $($d$)$:

$($a$)0\mathrm{.}070$

$($b$)0\mathrm{.}930$

$($c$)0\mathrm{.}465$

$($d$)0\mathrm{.}535$

Derive all the steps clearly to show how you arrived at the answer.