Let $x_{sd}$ and $x_{sd}$ be the normalized and unnormalized steepest descent directions at $x,$ for the norm $||*||.$ Prove the following identities.

$($a$)$ gradf$(x{)}^T{x}_{nsd}=-||gradf(x)|{|}_{**}$

$($b$)$ gradf$(x{)}^T{x}_{sd}=-||gradf(x)|{|}_{**}^2.$