HP Prime: Partial derivatives chain rule

diffchain

// diffchain by pineapples721
// Instructions
// 1. Create a CAS program.
// 2. Conenct your calculator to your PC. Launch the Connectivity Kit.
// 3. Paste this in to the new CAS program.

//2fns, 2vars
#cas
diff22(zfn,xfn,yfn):=
begin
  local dxds:=diff(xfn,s);
  local dxdt:=diff(xfn,t);
  local dyds:=diff(yfn,s);
  local dydt:=diff(yfn,t);
  local dzdx:=diff(zfn,x);
  local dzdy:=diff(zfn,y);
  local dzds:=0;
  local dzdt:=0;
  dzds:=(dzdx*dxds)+(dzdy*dyds);
  dzdt:=(dzdx*dxdt)+(dzdy*dydt);
  dzds:=subst(subst(dzds,x=xfn),y=yfn);
  dzdt:=subst(subst(dzdt,x=xfn),y=yfn);
  return {{"∂z/∂s",dzds},{"∂z/∂t",dzdt}};
end;
#end
//2fns, 3vars
#cas
diff23(zfn,xfn,yfn):=
begin
  local dxdr:=diff(xfn,r);
  local dxds:=diff(xfn,s);
  local dxdt:=diff(xfn,t);
  local dydr:=diff(yfn,r);
  local dyds:=diff(yfn,s);
  local dydt:=diff(yfn,t);
  local dzdx:=diff(zfn,x);
  local dzdy:=diff(zfn,y);
  local dzdr:=0;
  local dzds:=0;
  local dzdt:=0;
  dzdr:=(dzdx*dxdr)+(dzdy*dydr);
  dzds:=(dzdx*dxds)+(dzdy*dyds);
  dzdt:=(dzdx*dxdt)+(dzdy*dydt);
  dzdr:=subst(subst(dzdr,x=xfn),y=yfn);
  dzds:=subst(subst(dzds,x=xfn),y=yfn);
  dzdt:=subst(subst(dzdt,x=xfn),y=yfn);
  return {{"∂z/∂r",dzdr},{"∂z/∂s",dzds},{"∂z/∂t",dzdt}};
end;
#end
//3fns, 2vars
#cas
diff32(wfn,xfn,yfn,zfn):=
begin
  local dxds:=diff(xfn,s);
  local dxdt:=diff(xfn,t);
  local dyds:=diff(yfn,s);
  local dydt:=diff(yfn,t);
  local dzds:=diff(zfn,s);
  local dzdt:=diff(zfn,t);
  local dwdx:=diff(wfn,x);
  local dwdy:=diff(wfn,y);
  local dwdz:=diff(wfn,z);
  local dwds:=0;
  local dwdt:=0;
  dwds:=(dwdx*dxds)+(dwdy*dyds)+(dwdz*dzds);
  dwdt:=(dwdx*dxdt)+(dwdy*dydt)+(dwdz*dzdt);
  dwds:=subst(subst(subst(dwds,x=xfn),y=yfn),z=zfn);
  dwdt:=subst(subst(subst(dwdt,x=xfn),y=yfn),z=zfn);
  return {{"∂w/∂s",dwds},{"∂w/∂t",dwdt}};
end;
#end
//3fns, 3vars
#cas
diff33(wfn,xfn,yfn,zfn):=
begin
  local dxdr:=diff(xfn,r);
  local dxds:=diff(xfn,s);
  local dxdt:=diff(xfn,t);
  local dydr:=diff(yfn,r);
  local dyds:=diff(yfn,s);
  local dydt:=diff(yfn,t);
  local dzdr:=diff(zfn,r);
  local dzds:=diff(zfn,s);
  local dzdt:=diff(zfn,t);
  local dwdx:=diff(wfn,x);
  local dwdy:=diff(wfn,y);
  local dwdz:=diff(wfn,z);
  local dwdr:=0;
  local dwds:=0;
  local dwdt:=0;
  dwdr:=(dwdx*dxdr)+(dwdy*dydr)+(dwdz*dzdr);
  dwds:=(dwdx*dxds)+(dwdy*dyds)+(dwdz*dzds);
  dwdt:=(dwdx*dxdt)+(dwdy*dydt)+(dwdz*dzdt);
  dwdr:=subst(subst(subst(dwdr,x=xfn),y=yfn),z=zfn);
  dwds:=subst(subst(subst(dwds,x=xfn),y=yfn),z=zfn);
  dwdt:=subst(subst(subst(dwdt,x=xfn),y=yfn),z=zfn);
  return {{"∂w/∂r",dwdr},{"∂w/∂s",dwds},{"∂w/∂t",dwdt}};
end;
#end