`Derivative(f(z), For(z, a))`, rendered as $\left[ \frac{d}{d z}\, f\!\left(z\right) \right]_{z = a}$ or $f'(a)$, represents the derivative of $f(z)$ evaluated at $z = a$.

`Derivative(f(z), For(z, a, n))`, rendered as $\left[ \frac{d^{n}}{{d z}^{n}} f\!\left(z\right) \right]_{z = a}$ or ${f}^{(n)}(a)$, represents the order $n$ derivative of $f(z)$ evaluated at $z = a$.

The second argument $z$
defines a locally bound variable for the expression in the first argument. With the evaluation point set to $a = z$,

`Derivative(f(z), For(z, z))`may render more simply as $\frac{d}{d z}\, f\!\left(z\right)$.This operator is ambiguous since the intended meaning could be a real derivative, a complex derivative, or some other form of derivative. It is better to use

`RealDerivative`,`ComplexDerivative`,`ComplexBranchDerivative`, or`MeromorphicDerivative`.Definitions:

Fungrim symbol | Notation | Short description |
---|---|---|

Derivative | $\frac{d}{d z}\, f\!\left(z\right)$ | Derivative |

RealDerivative | $\frac{d}{d x}\, f\!\left(x\right)$ | Real derivative |

ComplexDerivative | $\frac{d}{d z}\, f\!\left(z\right)$ | Complex derivative |

ComplexBranchDerivative | $\frac{d}{d z}\, f\!\left(z\right)$ | Complex derivative, allowing branch cuts |

MeromorphicDerivative | $\frac{d}{d z}\, f\!\left(z\right)$ | Complex derivative, allowing poles |

Source code for this entry:

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