I am going through a proof which includes the following lines:
$\nabla g(x^k) \big(g(x^k) + \nabla g(x^k)^T(x^{k+1}-x^k)\big) = 0$
$\nabla g(x^k) g(x^k) + \nabla g(x^k) g(x^k)^T(x^{k+1}-x^k)\big) = 0$
It's not quite clear to me why for the second term it says:
$\nabla g(x^k) g(x^k)^T$ and not $\nabla g(x^k)\nabla g(x^k)^T$
Is there some kind of identity which can be used here?