# How do I calculate the partial derivative with respect to $x$?

I am trying to implement CNN using python Numpy.
I searched so much, but all I found was for one filter with one channel for Convolution.

Suppose we have an X as Image with this shape: (N_Height, N_Width, N_Channel) = (5,5,3)

And Let's say I have 16 filters with this shape: (F_Height, F_Width, N_Channel) = (3,3,3) , stride=1 and padding=0

Forward:

Output shape after conv2d will be

(
math.floor((N_Height - F_Height + 2*padding)/stride + 1 )),
math.floor((N_Width- F_Width + 2*padding)/stride + 1 )),
filter_count
)

So the output of this layer will be an array with this shape: (Height, Width, Channel) = (3, 3, 16)

BackPropagation:

Suppose $$dL/dh$$ is the input for my layer in backpropagation with this shape: (3,3,16)

Now I must find $$dL/dw$$ and $$dL/dx$$: $$dL/dw$$ to update my filters params and $$dL/dx$$ to pass it as input to the previous layer as Loss respect to the input X.

From this answer Error respect to filters weights I found how to calculate $$dL/dw$$.

The problem I have in BackPropagation is I don't know how to calculate $$dL/dx$$ having this shape:(5,5,3) and pass it to the prev layer.

I read lots of articles in Medium and other sites but I don't get how to calculate it: