17.5.18 Chain Rule Example

    


Part A - We start with a strait forward application of the chain rule. 
        
because is not a function of t directly, we need extra terms to link z throw its intermediate variables to the objective t.


Part B  - next, with  this implies that .

Thus,
         

And so what we started in part a:
         

simplifies:
        
        
        
and that's it





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