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Let x = [1, 1]T , y = [1, 1]T ∈ R 2 and let f...

Let x = [1, 1]T , y = [1, 1]T ∈ R 2 and let f : R 2 =⇒ R 2 with f(z) =z1.x + z2.y for any z = [z1, z2] T ∈ R 2 . Further, z = g(r) = [r 2 , r3 ] where r ∈ R . Show how chain rule is applied here giving major steps of the calculation, write down the expression for ∂f ∂r , and also evaluate ∂f/ ∂r at r=2.

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