I don&#x27;t think that this is quite the right explanation.<p>|y - wx| isn&#x27;t differentiable but it is subdifferentiable.  So the derivative is defined at every point except where y = wx, and in that case you&#x27;re more or less fine if you just pretend that the derivative is zero at that point.<p>One reason why squaring is preferred is that the derivative has a nice closed form, which can be used to find closed form solutions.<p>Another is that people like to fit their models with gradient descent, and gradient descent has better guarantees for strongly convex loss functions.  It also works better in practice.  Intuitively: if you try to minimize x^2 by gradient descent, you have the largest gradients when you&#x27;re far from the minimum.  If you try to minimize |x|, then your gradient is always either +1 or -1, making it harder to converge around the minimum.  See the Huber loss for a strongly convex relaxation of the absolute value function.