I'm just curious, so is there a word that you could use to express that a mathematical function has a derivative?

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    The word is "differentiable". – Peter Shor Apr 3 '15 at 19:24
  • Right. And the process of calculating the derivative of a function is called differentiation. – John Lawler Apr 3 '15 at 19:35

Introduction to Differential Calculus: Systematic Studies ... Ulrich L. Rohde, ‎G. C. Jain, ‎Ajay K. Poddar - 2012

If a function has a derivative at x1 of its domain, then it is said to be differentiable at x1 ... Differentiable Function: If a function is differentiable at every number in its domain, it is called a differentiable function.

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