Suppose we have all diffeomorphisms, $G,p,R,\phi,F$ with suitable domain and range, and we are given that, $G\circ p=R\circ \phi$,$w=p(z),u=\phi(z)$, suppose there is a transformation $Dp(z):(\sigma,t)\mapsto(\sigma,-\frac{1}{2}a_{*}t)$, and $D\phi(z):(\sigma,t)\mapsto (\sigma+t,\frac{1}{2}a_{*}t)$, now could any one tell me what will be the derivative of $G=R\circ\phi\circ F$ at point $w_*$
My start:
Applying Derivative Operator both side we get $DG(w)\circ Dp(z)=DR(u)\circ D\phi(z)$
