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\begin{align*}
p \,  (\nu_H(b)-D)
&=p \, (\tilde{\nu}(b,a)-\tilde{D})
&&\Rightarrow  \tilde{D} = \delta (b , D ,a) , \\ 
b \, (\mu(s) - D) - \alpha \nu_H (b) p &=
b \, (\mu(\tilde{s}) - \tilde{D}) - \alpha \tilde{\nu}(b,a)p   
&&\Rightarrow \tilde{s}  = \sigma (p , b , s, a), \\ 
%%%%%%%%%%%%%%%From Here%%%%%%%%%%%%%%%%
\frac{\partial \sigma}{\partial p} p \, (\nu_H (b) - D) + \frac{\partial \sigma}{\partial b} (b(\mu(s)-D)
- \alpha \nu_H(b) p) 
+ \frac{\partial \sigma}{\partial s} \big(D(s_F -s ) - 
\beta_\mu(s)b\big)
\\
 %%%%%%%%%%%%%%%%To Here%%%%%%%%%%%%%%%%%%%%%%%
&= 
\tilde{D} \, (\tilde{s}_F - \tilde{s}) - \beta_\mu(\tilde{s}) \tilde{b} 
&&\Rightarrow 
\tilde{s}_F
= \sigma_F (p,b,s,s_F , a)
 \end{align*}
 
\end{document}