Lipschitz Continuity and Lipschitz Constant of a Multidimensional Function

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I have a function $f: \mathbb{R}^n \to \mathbb{R}$ defined as follows:

$$ f(x_1,\dots,x_n) = -\frac{x_j-c_j}{(1-k_j)^2}e^{ -\frac{1}{2}\sum_{i=1}^n\left(\frac{x_i-c_i}{1-k_i}\right)^2} $$

for $j \in \{1,\dots,n\}$

$c_1,\dots,c_n$ and $k_1,\dots,k_n$ are constants.

I am interested in determining whether this function is Lipschitz continuous and, if so, finding its Lipschitz constant.

Can anyone provide insights or a proof regarding the Lipschitz continuity of this function? Additionally, any help in calculating the Lipschitz constant would be greatly appreciated.

Thank you in advance for your assistance!