Exercise 17.3. Letf : 1:522 > R2 be the function rs, y) = (y? y,a:y3 as), so f(1, 1) = (0.0). By using the Chain Rule to compute DU' 0 f)(11 1), give the linear approximation to (f o f)(1 + .31,1 1 + k) for h,k near 0. (If you try to compute (f o f)(a:,y) = f(f(:c,y)) explicitly with the aim of directly computing its partial derivatives at (1, 1), you will get a total mess! This illustrates one important role for the multivariahle Chain Rule in the machine learning algorithm called hackpropagation that is discussed in Appendix G; see in particular the nal paragraph of Section (3.4.)