$f(t, \begin{bmatrix}x\_1\\x\_2\end{bmatrix}, u)=e^{-|u|^2}\begin{bmatrix}x\_1\\x\_2\end{bmatrix},$ where $f:[0, 3]\times \mathbb{R}^2\times \mathbb{R}\rightarrow \mathbb{R}^2$ is a given nonlinear function. I want to find the Lipschitz constants for this function w.r.t second and third arguments. Lipschitz continuity definition w.r.t second and third arguments is $\|f(t, \begin{bmatrix}x\_1\\x\_2\end{bmatrix}, u)-f(t, \begin{bmatrix}y\_1\\y\_2\end{bmatrix}, v)\|\leq a\|\begin{bmatrix}x\_1\\x\_2\end{bmatrix}-\begin{bmatrix}y\_1\\y\_2\end{bmatrix}\|+b|u-v|, $ where a and b are the Lipschitz constants. I want to find the smallest of these.