Let R R." be thefunction given by f(x, y) = (e2+2xy, x cos(y2 - 1), sin(a2 - y? ) ). (a) Let P be a point in the domain of f. As we saw in class, for (x, y) near P, we have f ( x, y) ~ f ( P) + ( Dpf) (h), where h = (, y) - P. The expression on the right hand side is called the linear approximation of f around P. Compute the linear approximation of our function f around the point P = (1, -1).\f(b) Consider now the function g : R3 > R2 given by 9(x, y, z) = (ln(1 + 3:2 + y2 + 22], at: yz). Since the range of f is a subset of the domain of 9, we can consider the composition 9 O f : R,2 > R2. As the composition of smooth functions, 9 o f is smooth. Its derivative is a linear map R2 > R2. so it is represented by a 2 x 2 matrix [with respect to the standard basis of R2}. Use the chain rw'e to compute this matrix representing the derivative of g 0 f at the point P = (l, l)