Differentiability is the mathematical property of a function having a well-defined derivative at every point in its domain, allowing gradients to be computed via calculus. In machine learning it is a prerequisite for gradient-based optimisation: activation and cost functions must be differentiable, or approximately so, for backpropagation to compute parameter updates. Non-differentiable operations require relaxations, subgradients, or surrogate approximations to remain trainable.