Considering the function below, where log is the natural logarithm withx=x1(logx) and e = exp(1) 2.718.

1) Write down the following partial derivatives.

xf; yf; x22f; y22f;xy2f

2) Write down the two-dimensional Taylor series of f(x, y) about the point (x₀, y₀) where x₀ = 0 and y₀ = e. Try including all terms up to first order.

3) Write down the two-dimensional Taylor series of f(x, y) about the point (0, 0). Try including all terms up to second order.