Derivative after subtracting a simple pole: $\bigl(f - \tfrac{A}{z - p}\bigr)'(x) = f'(x) + \tfrac{A}{(x-p)^2}$

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Derivative after subtracting a simple pole: $\bigl(f - \tfrac{A}{z - p}\bigr)'(x) = f'(x) + \tfrac{A}{(x-p)^2}$ · Prove2Me