Consider the diagram for the LSTM cell below:

For example for update gate we will have:

${}_u^{(\text{:}t\text{:})}=W_u\left[\begin{array}{c}{a}^{?}\end{array}\right]$

$x$

$+b_u$

${}_u^{?}=({}_u^{?})$

$W_u=\left[\begin{array}{cc}{W}_{ua}& W_{ux}\end{array}\right]$

$x^{?}=\left[\begin{array}{cccccc}{x}_0& x_1& \text{d}\text{o}\text{t}\text{s}& x_i& \text{d}\text{o}\text{t}\text{s}& x_n\end{array}\right]$

A$.$ Calculate c$^$ a$^$ and $^$ with respect to inputs weights and biases.$(2$points$)$

B$.$ Suppose we have the value of y$^$ and the input gradients from cell above danext and dcnext.

ATso

del$\frac{L}{d}$elz$=-$yand

del$\frac{L}{d}$ela$=$del$\frac{L}{d}$ela$+$ danext

Now perform the backpropagation for the weights and biases. $(4$ points$)$