Chapter 13 - Partial Derivatives - 13.5 The Chain Rule - Exercises Set 13.5 - Page 957: 16

The answer is the explanation on the "work step by step" section.

We can express $f(x)=x^{x}$ implicitly as a function of two variables, y and z, as in the picture, calling y=z=x. Doing that we find the derivative is the sum of partial derivatives. In the y derivative we have the power rule, and in the z derivative we treat as exponential function.