Please fill in where there are question marks, and do not alter any existing code:

sigma $=$ np$.$tanh

# Let's use a random initial weight and bias.

W $=$ np$.$array$([[-0\mathrm{.}94529712,-0\mathrm{.}2667356,-0\mathrm{.}91219181],$

$[2\mathrm{.}05529992,1\mathrm{.}21797092,0\mathrm{.}22914497]])$

b $=$ np$.$array$([0\mathrm{.}61273249,1\mathrm{.}6422662])$

# define our feed forward function

def a$1($a$0)$ :

# Notice the next line is almost the same as previously,

# except we are using matrix multiplication rather than scalar multiplication

z $=???$

# Everything else is the same though,

return sigma$($z$)$

# Next, if a training example is$,$

x $=$ np$.$array$([0\mathrm{.}7,0\mathrm{.}6,0\mathrm{.}2])$

y $=$ np$.$array$([0\mathrm{.}9,0\mathrm{.}6])$

# Then the cost function is$,$

d $=???$ # Vector difference between observed and expected activation

C $=???$ # Absolute value squared of the difference.

sigma $=$ np$.$tanh

# Next define the feed$-$forward equation.

def a$1($w$1,$ b$1,$ a$0)$ :

z $=???$

return sigma$($z$)$

# This function returns the derivative of the cost function with

# respect to the weight.

def dCdw $($w$1,$ b$1,$ x$,$ y$)$ :

dCda $=???$ # Derivative of cost with activation

dadz $=???$ # derivative of activation with weighted sum z

J $=???$

dzdw $=???$# derivative of weighted sum z with weight

J $=???$

return J # Return the chain rule product.

# This function returns the derivative of the cost function with

# respect to the bias.

# It is very similar to the previous function.

# You should complete this function.

def dCdb $($w$1,$ b$1,$ x$,$ y$)$ :

dCda $=???$

dadz $=???$

# Change the next line to give the derivative of

# the weighted sum, z$,$ with respect to the bias, b$.$

dzdb $=???$

return dCda $*$ dadz $*$ dzdb

dCdb $($W$,$ b$,$ x$,$ y$)$

array$([[-2\mathrm{.}19184549$e$+00],$

$[1\mathrm{.}42277240$e$-03]])$

dCdw $($W$,$ b$,$ x$,$ y$)$

array$([[-1\mathrm{.}53429185$e$+00,-1\mathrm{.}31510730$e$+00,-4\mathrm{.}38369099$e$-01],$

$[9\mathrm{.}95940681$e$-04,8\mathrm{.}53663441$e$-04,2\mathrm{.}84554480$e$-04]])$