Quiz (Chain Rule)

Show all work and justify each step.

(1) Differentiate the following functions. Show all steps.
    
    (a)
    
    (b)
    
    (c)

(2) If where is a differentiable function, find

(3) Suppose is a differentiable function on Let and Find expressions for and

(4) Determine if the following statement is true or false. Then justify your claim.
If is a differentiable function of is a differentiable function of and is a differentiable function of then


    
(5) Let be a differentiable function of Use to prove that



when Use the formula to find given

(6) Show that What do you think is the importance of the exercise?

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