What phase rotation occurs when you take the derivative of an audio signal?
Simple Fourier Transform propery for differentiation is
$$\mathcal{F}\{\frac{\partial}{\partial t}x(t)\}=j\omega \cdot\mathcal{F}\{x(t)\}$$
Differentiation in time corresponds to multiplication with $j\omega$ in frequency. Hence the +6dB/octave slope. The phase shift is a constant 90 degrees for all frequencies.