# Differentiable function

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A function f(x) is **differentiable** at the point *a* if and only if, as *x* approaches *a* (which it is never allowed to reach), the value of the quotient:

approaches a limiting value that we call the derivative of the function f(x) at *x=a*.

There is also the more rigorous definition: a function f is said to be differntiable at point *a* if ∀ ∃ such that if

then

- .