## Second-Order Directional Derivative

If I could get some help on this problem, thank you:

The equation x/z = ln(z/y) + 1 defines implicitly z as a function of x and y in the neighbourhood of a=(1,1,1) (why?) so that z=f(x,y). Find the second-order directional derivative of f at the point (1,1) in the direction (1/sqrt(2),-1/sqrt(2)).