Assume linear model: ( \haty = w x + b ) Loss (MSE) over N samples: ( L = \frac1N \sum_i=1^N (y_i - (w x_i + b))^2 )
def loss_slope(x): return 2 * x
For functions of multiple variables ( f(x_1, x_2, ..., x_n) ), a partial derivative ( \frac\partial f\partial x_i ) treats all other variables as constants.