A partial derivative measures how a function changes with respect to one variable while holding all other variables constant. Written ∂f/∂x for the partial derivative of f with respect to x.

Neural network loss functions depend on millions of weights. ∂L/∂wi isolates how much the loss changes when only weight wi changes - treating all other weights as constants. The gradient is the vector of all partial derivatives. Computing partial derivatives for all weights efficiently is exactly what automatic differentiation (autograd in PyTorch, TensorFlow) does.