The derivative in inverse matrix.

I wonder how to calculate the following derivative w.r.t to the array: $$frac {d (x ^ TW ^ {- T} W ^ {- 1} x)} {dW}$$, where $$W$$ is a $$mathbb {R} ^ {d times d}$$ matrix and $$x$$ is a $$mathbb {R} ^ d$$ vector. The result must be a $$mathbb {R} ^ {d times d}$$ matrix.