title: Partial derivative for mean absolute error
body: <p>What is the partial derivative for MAE? I understand that for mean squared error (MSE) the partial derivative with respect to some <code>x1</code>  would be <code>-x1 * (y_pred - y_actual)</code> assuming the the following version of MSE is used.</p>
  <p><a href="https://i.stack.imgur.com/oRjTt.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/oRjTt.png" alt="ML MSE function" /></a></p>
  <p>What is the partial derivative for <code>x1</code> when the loss function is MAE instead of MSE? I've been trying to find this but I haven't had any luck. Would it just be <code>-(y_pred - y_actual)</code> when <code>x1</code> is greater than 0, and <code>(y_pred - y_actual)</code> when <code>x1</code> is less than 0? Or is there something else that I'm missing?</p>