Lecture 16: The chain rule Nathan Pueger 16 October 2013 1 Introduction Today we will add one more rule to our toolbox. This rule concerns functions that are expressed as ...
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...Lecture the chain rule nathan pueger october introduction today we will add one more to our toolbox this concerns functions that are expressed as composi tions of idea a composition is you can sometimes interpret function sequence two steps allows dierentiate be dierentiating individually and multiplying results allow us compute great deal derivatives especially when it used in conjunction with other rules reference for stewart basic underlies faster inputs change its outputs so example if f x another then second moving twice fast rst s derivative magnied by factor d dx generalizes principle there standard ways write which named after mathematicians usually credited inventing calculus newton notation leibniz dz dy g here symbol means not multiplication feed from into just same thing y should refer something z therefore also at glance all obvious how these statements related show they both work i illustrate them sin let sinx dsin cos cases have composite formed plugging output input pre...