Definition:Derivative/Real Function/Derivative at Point

Definition
Let $I$ be an open real interval.

Let $f: I \to \R$ be a real function defined on $I$.

Let $\xi \in I$ be a point in $I$.

Let $f$ be differentiable at the point $\xi$.

Also denoted as
The derivative of $f$ at the point $\xi$ is variously denoted:


 * $f' \left({\xi}\right)$


 * $D f \left({\xi}\right)$


 * $D_x f \left({\xi}\right)$


 * $\dfrac {\mathrm d} {\mathrm d x} \left({\xi}\right)$

If the derivative is with respect to time:


 * $\dot f \left({\xi}\right)$

is sometimes used.

Also see

 * Equivalence of Definitions of Derivative