How to implement a derivative of a unitary gate in a quantum circuit?

I was reading this paper¹, which says in Eqn(15) that the derivative of a unitary gate with respect to the parameter $mu$ can be decomposed into linear combinations of unitary gates.
However, I didn’t understand how to determine the coefficient, $alpha$ in there.
I want to implement a derivative operation in a quantum circuit. Could anyone help with the proof of that statement in Eq(15)?

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¹Reference: M. Schuld, V. Bergholm, C. Gogolin, J. Izaac, and N. Killoran, "Evaluating analytic gradients on quantum hardware", Phys. Rev. A 99, 032331 (2019), arXiv:1811.11184.