We have read that Jesus is God. How could the man Jesus die but not Jesus the God? First off, natures cannot die, whether human or divine, because they are the essence, character and attributes of the person, not the person. The divine Persons cannot die, for they were "before the beginning and after the end". The spirits of the saints given to them by God will not die. The spirits of the condemned will "die" only so much as they will not be alive eternally in the presence of God. So, only human flesh and bone can die by mortal death. Peter offers a hint of understanding, "For Christ died for sins once for all, the Righteous for the unrighteous, that He might bring us to God. In His human body He was put to death, but He was made alive by the Holy Spirit, by which He went and preached to the disobedient spirit beings who have been held in prison for the day of their condemnation."
At the moment of death, Jesus' human nature ceased to have any effect upon His physical body. His divine nature, which all the while rendered Him the Son of God, no longer had to work within the human limitations of His physical body. He was freed from the bonds of this world. Of course, soon after, He was resurrected.
Some believe that His sacrificial burden was so incomprehensible, there is no way He could have endured it as a mere man. While many saintly martyrs have since suffered the same or worse physical torture and pain, none could withstand the smallest fraction of time being perfectly righteous and pure, yet being tainted and polluted with the sins of the world. The only way we can comprehend this humility is by understanding that Jesus had full expectation of His resurrection and the ultimate impact it would have.
Others believe that if Jesus as God did not die along with Jesus the man, His was just a human sacrifice, no more effective in taking away sin than an animal sacrifice. But Jesus' sacrifice was infinitely more effective than that of a mere man, because He was the Son of Man. Also, animals do not have the cognitive thinking and reasoning to overcome temptation or lay down their own lives in obedience to God. This view also completely ignores the sacrifices that Triune ordained before Jesus the child was born. He allowed Himself to be stripped of all rightful honor and glory, humbled Himself in human flesh, while remaining perfectly obedient to God's will by becoming the ultimate servant to mankind through a life of suffering. There will never be any greater sacrifice!