Risk-free Rate, CML and SML

Capital Market Line (CML) is the best possible capital allocation line (CAL) which is tangent to a broad market portfolio (constructed via Optimal Risky Portfolio with a broad input-list or index) of risky assets or Market Portfolio.
CML 
\(E\left(r_p\right)=r_f+\frac{\sigma_p\left[E\left(r_m\right)-r_f\right]}{\sigma_m}\)

Differentiating w.r.t \(r_f\)

\(\frac{\partial E\left(r_p\right)}{\partial r_f}=\left(1-\frac{\sigma_p}{\sigma_m}\right)\)

We'll consider two cases here -