Chain Reactions

Chain Rule

2 Corinthians 5:16-21 NKJV

Therefore, from now on, we regard no one according to the flesh. Even though we have known Christ according to the flesh, yet now we know Him thus no longer. Therefore, if anyone is in Christ, he is a new creation; old things have passed away; behold, all things have become new. Now all things are of God, who has reconciled us to Himself through Jesus Christ, and has given us the ministry of reconciliation, that is, that God was in Christ reconciling the world to Himself, not imputing their trespasses to them, and has committed to us the word of reconciliation. Now then, we are ambassadors for Christ, as though God were pleading through us: we implore you on Christ’s behalf, be reconciled to God. For He made Him who knew no sin to be sin for us, that we might become the righteousness of God in Him.

Once students have seen the chain rule for differentiation of composed functions, it is natural to extend the chain rule to nested functions, where there is more than two functions that are composed.  Fun problems to investigate are ones that are repeated applications of the same function.  Try differentiating tan(tan(tan(tan(tan x)))) or ln(ln(ln(ln(ln(ln x))))), for example.  Working your way from the outside to the inside yields a derivative which is product chain of related functions. 

In a similar way, when we interact with other people there is a chain reaction to our behavior.  Most people believe that abused children are more likely to become abusers themselves someday, for example.  Less dramatic behavior also can have a reaction that extends beyond the initial engagement.  A popular Warner Brothers film of 2000 Pay it Forward (based on a novel with the same name by Catherine Ryan Hyde) depicts how a chain of reactions to an initial act of kindness can change an entire community.  Christians need to be specially mindful of this chain reaction, since we are ambassadors for Christ.  Our verbal and nonverbal witness can yield unexpected results, especially under the influence of the Holy Spirit.