r"""
        :math:`\frac{\partial \hat{\rho''}(\omega)}{\partial \tau} = \rho_0
        \frac{-m \omega^c c \tau^{c-1} sin(\frac{c \pi}{2} }{1 + 2 (\omega
        \tau)^c cos(\frac{c \pi}{2}) + (\omega \tau)^{2 c}} +
        \rho_0 \frac{\left[-m (\omega \tau)^c sin(\frac{c \pi}{2}
        \right] \cdot \left[ 2 \omega^c c \tau^{c-1} cos(\frac{c
        \pi}{2}) + 2 c \omega^{2 c} \tau^{2 c - 1}\right]}{\left[1 + 2 (\omega
        \tau)^c cos(\frac{c \pi}{2}) + (\omega \tau)^{2 c}\right]^2}`

def dim_dtau(self, pars):
        r"""
        :math:`\frac{\partial \hat{\rho''}(\omega)}{\partial \tau} = \rho_0
        \frac{-m \omega^c c \tau^{c-1} sin(\frac{c \pi}{2} }{1 + 2 (\omega
        \tau)^c cos(\frac{c \pi}{2}) + (\omega \tau)^{2 c}} +
        \rho_0 \frac{\left[-m (\omega \tau)^c sin(\frac{c \pi}{2}
        \right] \cdot \left[ 2 \omega^c c \tau^{c-1} cos(\frac{c
        \pi}{2}) + 2 c \omega^{2 c} \tau^{2 c - 1}\right]}{\left[1 + 2 (\omega
        \tau)^c cos(\frac{c \pi}{2}) + (\omega \tau)^{2 c}\right]^2}`
        """
        self._set_parameters(pars)
        # term1
        nom1 = - self.m * np.sin(self.ang) * self.w ** self.c *\
            self.c * self.tau ** (self.c - 1)
        term1 = nom1 / self.denom

        # term2
        nom2 = (self.m * self.otc * np.sin(self.ang)) *\
            (2 * self.w ** self.c * self.c * self.tau ** (self.c - 1) *
             np.cos(self.ang) + 2 * self.c * self.w ** (2 * self.c) *
             self.tau ** (2 * self.c - 1))
        term2 = nom2 / self.denom ** 2

        result = term1 + term2
        result *= self.rho0
        return result