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

def dim_dc(self, pars):
        r"""
        :math:`\frac{\partial \hat{\rho''}(\omega)}{\partial c} = \rho_0
        \frac{-m sin(\frac{c \pi}{2}) ln(\omega \tau)(\omega \tau)^c - m
        (\omega \tau)^c \frac{\pi}{2} cos(\frac{\pi}{2}}{1 + 2 (\omega \tau)^c
        cos(\frac{c \pi}{2}) + (\omega \tau)^{2 c}} + \rho_0 \frac{\left[-m
        (\omega \tau)^c cos(\frac{c \pi}{2}) \right] \cdot \left[ -2 ln(\omega
        \tau) (\omega \tau)^c cos(\frac{c \pi}{2}) + 2 (\omega \tau)^c
        \frac{\pi}{2} cos(\frac{c \pi}{2}) \right] + \left[2 ln(\omega \tau)
        (\omega \tau)^{2 c}\right]}{\left[1 + 2 (\omega \tau)^c cos(\frac{c
        \pi}{2}) + (\omega \tau)^{2 c}\right]^2}`
        """
        self._set_parameters(pars)
        # term1
        nom1a = - self.m * np.log(self.w * self.tau) * self.otc *\
            np.sin(self.ang)
        nom1b = - self.m * self.otc * (np.pi / 2.0) * np.cos(self.ang)
        term1 = (nom1a + nom1b) / self.denom

        # term2
        nom2 = (self.m * self.otc * np.sin(self.ang)) *\
            (2 * np.log(self.w * self.tau) * self.otc * np.cos(self.ang) -
             2 * self.otc * (np.pi / 2.0) * np.sin(self.ang) +
             2 * np.log(self.w * self.tau) * self.otc2)
        term2 = nom2 / self.denom ** 2
        result = term1 + term2

        result *= self.rho0
        return result