Gradient Vector

**tttcomrader** · April 20th 2009, 04:27 PM

Find the gradient vector of $f(x) = e^ { ||x||^2}$ for $x \in \mathbb {R} ^n$

I'm not sure if I understand how to take derivative of the norm of x.

Thanks.

**TheEmptySet** · April 20th 2009, 05:36 PM

Originally Posted by tttcomrader

Find the gradient vector of $f(x) = e^ { ||x||^2}$ for $x \in \mathbb {R} ^n$

I'm not sure if I understand how to take derivative of the norm of x.

Thanks.

Maybe this will help

$||x||^2=x_1^2+x_2^2+...+x_n^2$

$\frac{\partial f}{\partial x_i}=2x_ie^{||x||^2}$

so we get

$\nabla f =2e^{||x||^2}(x_1,x_2,x_3,...,x_n)$

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