# Thread: whats the derivative of this function

1. ## whats the derivative of this function

$f(x) : R^{a} \longrightarrow R, f(x)=||x||,$ with || . || euclidean norm

2. Originally Posted by silversand
$f(x) : R^{a} \longrightarrow R, f(x)=||x||,$ with || . || euclidean norm
Notice that $f(x_1,...,x_n) = \sqrt{x_1^2+....+x_n^2}$.
Therefore, $\nabla f = \left( \frac{x_1}{\sqrt{x_1^2+...+x_n^2}}, ... , \frac{x_n}{\sqrt{x_1^2 + ... + x_n^2}} \right)$, so $\nabla f(\bold{x}) = \frac{\bold{x}}{|\bold{x}|}$.