Considering the function w(x, y) = x(y 1)² ln (1 x), where ln is the natural logarithm.

(a) Write all partial derivatives of the function up to the second order

(b) Write the two-dimensional Taylor series of the function about the point (0, 0) including all terms up to second-order including the terms that are up to the quadratic terms.

(c) Write the two-dimensional Taylor series of the function about the point (1, 1) including all terms up to first-order including the terms that are up to the linear terms.