Trouble finding the derivative of an optimization function

How can I derivate the following optimization function?

$$L=sum_{u,i}(y_{u,i}-v_ix_u)^2+lambdaleft(sum_i|v_i|_2^2+sum_u|x_u|_2^2right)$$

I just want to get the equations of the gradient descent method, so I want to get the partial derivative of $L$ with respect to $v$ and the partial derivative of $L$ with respect to $x$. This function is similar to ridge regression function.

I just know how to calculate the first of the term of the function, but I have trouble to derive the second addend of the function:

$$delta v_i^k L=-2sum_i(y_{u,i}-v_i x_u)x_u^k + ¿?$$
$$delta x_i^k L=-2sum_i(y_{u,i}-v_i x_u)v_u^k + ¿?$$