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.