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A function is differentiable if it has a defined derivative for every input, or

$ \lim_{h\to0}\frac{f(x+h)-f(x)}{h}=a $

for every x. A function will be differentiable iff it follows the Weierstrass-Carathéodory criterion for differentiation.

Differentiability is a stronger condition than continuity; and differentiable function will also be continuous.

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