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

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

Thanks.

2. Originally Posted by tttcomrader
Find the gradient vector of $\displaystyle f(x) = e^ { ||x||^2}$ for $\displaystyle x \in \mathbb {R} ^n$

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

Thanks.
Maybe this will help

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

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

so we get

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