Quiz (Chain Rules)

Show all work and justify each step.

(1)  Use the chain rule for one parameter with

    (a) where and
    
    (b) where and

(2) Use the chain rule for two parameters with

    (a) where and
    
    (b) where and

(3) Let lie on the ellipsoid without solving for find and

(4) If show that

(5) If show that

(6) Let be a differentiable function of , where Show that