$x \in \mathbb{R}^n$ How to find gradient of $f(x) = -e^{-x^Tx}$
2026-03-30 21:09:53.1774904993
How to find gradient of the function
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$$-x^Tx = -(x_1^2+x_2^2+...+x_n^2)$$
$$-e^{-x^Tx} = -e^{-(x_1^2+x_2^2+...+x_n^2)}$$
$$\frac{\partial(-e^{-x^Tx})}{\partial x_i} = 2x_ie^{-(x_1^2+x_2^2+...+x_n^2)} = 2x_ie^{-x^Tx}$$