I am trying to understand a step in the math given a scientific paper. They differentiate an objective function of the form:
$snr = \frac{\sum_{i=1}^n x_it_i}{\sum_{i=1}^n x_id_i} $
To maximize this function they partially differentiate this function with respect to $x_i$.
$\frac{\partial{snr} }{\partial{x_i}} = \frac{\dfrac{t_i}{d_i}-\frac{\sum_{j=1}^n x_jt_j}{\sum_{j=1}^n x_jd_j}}{\frac1{d_i}\sum_{j=1}^n x_jt_j} $
any clues as to how to go that step will help im pretty lost.....