What do I do once I have the Jacobian Matrix from Softmax Derivative

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I am teaching myself Artificial Intelligence from scratch without libraries

I have a decent handle on most of it

UPDATE-EDIT

I am lost however on the next step mathematically after deriving the softmax activation function

as an example to hopefully clarify

lets call Softmax Derivative dSM and if that is the name of the function and the index of the value outputted is i

then it would be dSM_i

when the index i is equal to k which i will define as the ground truth vector index

then

the matrix would look like

(dSM_i * (1 - dSM_i)) (-dSM_i * dSM_k) (-dSM_i * dSM_k)
(-dSM_i * dSM_k) (dSM_i * (1 - dSM_i)) (-dSM_i * dSM_k)
(-dSM_i * dSM_k) (-dSM_i * dSM_k) (dSM_i * (1 - dSM_i))

but I dont know what to do from there

how do i go from there to the equation

derivative Of sum of loss w.r.t derivative of activation
multiplied by
derivative of activation w.r.t derivative of input
multiplied by
derivative of input w.r.t derivative of weight

each row of the jacobian matrix has 3 values when all I need has is 1

Please someone help Thanks I cant find anything yet just how to get to the place i can get to already