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Definition

Valued in fields

Given a calculus field?algebraic limit field $F$, a subtype $S \subseteq F$, a pointwise continuous function $f:C^0(S, F)$ is differentiable if the difference quotient has a limit approaching the diagonal

Let us define the type of differentiable functions $D^1(S, F)$ on $S$ as the type of pointwise continuous functions that are differentiable.

See also

• pointwise continuous function
• Newton-Leibniz operator
• iterated differentiable function
• smooth function
• directionally differentiable function