modern portfolio theory - What’s the derivative of the sharpe ratio for one asset? Trying to optimize on it for a model

It seems most Sharpe ratio derivations seem to be for portfolios but I am just tracking a single asset?

$SR = (r_p - r_f) / \sigma_p$ but what would I derive with respect to for an optimization/ automated use case?

I am trying to understand how they use the Sharpe Ratio in this paper:

"Algorithm Trading using Q-Learning and Recurrent Reinforcement Learning", by Xin Du, Jinjian Zhai, Koupin Lv.