Use the properties of differentiation in Problem1.11 to prove (1.13) and (1.14).

Problem1.11

 To prove (1.13) and (1.14).

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1.11 Let f (0) be an x1 and g (0) a 1 xm vector-valued function of 0 = (01,..., 0q). The derivatives off and g are defined as follows: afi afn 01 801 f= 80 afi afn 80 qxn 1 ... 201 91 q g= " 80 agm 1 mxq (1.30) Thus, g=(g). As a special case, if (0) is a scalar function, it follows from (1.30) that a = T 4) is a q1 column vector. Let A be a mxn matrix of constants, g (0) a m x 1 vector-valued function of 0, and h (e) a function of 0. Then, we have the following: