Definition:Derivative/Real Function/Derivative on Interval

Definition
Let $f$ be a real function defined on an open interval $I$.

Let $f$ be differentiable on the interval $I$.

Then $f^\prime: I \to \R$ is defined as the real function whose value at each point $x \in I$ is $f^\prime \left({x}\right)$.

It can be variously denoted as:
 * $\dfrac {\mathrm d f}{\mathrm d x}$


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


 * $f^\prime \left({x}\right)$


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


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