How can I find the gradient of a non linear SVM wrt input?

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Given that an SVM will have the following function: enter image description here

And if I was to use a kernel, this would become:

enter image description here

Where the kernel can be the Gaussian kernel:

enter image description here

How Would I go about finding its gradient wrt the input? I need to know this as to then apply this to a larger problem of a CNN with its last layer being this SVM, so I can then find the gradient of this output wrt the input of the CNN.