Matrix exponent differentiation

Question

Given $f(x) = x^T\exp(xx^T)x$, where $x \in \mathbb{R}^n$, find the $\nabla_xf(x).$

Note: $\exp(A) = \displaystyle\sum\limits_{k=0}^{\infty}\dfrac{A^k}{k!}$, $A \in \mathbb{R^{n\times n}}$

Answer 1

Hint: $x^T(xx^T) ^kx=(x^Tx) ^{k+1}$. And $x^Tx$ is just a number, not a vector/matrix.