نمادگذاری‌های مشتق

${\displaystyle \frac{d^{n}y}{d{x}^n},\frac{d^n(f(x))}{d{x}^n},\text{ or }\frac{d^n}{d{x}^n}(f(x))}$

${\displaystyle \mathrm{\nabla }=\left(\frac{\mathrm{\partial }}{\mathrm{\partial }x},\frac{\mathrm{\partial }}{\mathrm{\partial }y},\frac{\mathrm{\partial }}{\mathrm{\partial }z}\right)}$

${\displaystyle \mathrm{g}\mathrm{r}\mathrm{a}\mathrm{d}\phi =\left(\frac{\mathrm{\partial }\phi }{\mathrm{\partial }x},\frac{\mathrm{\partial }\phi }{\mathrm{\partial }y},\frac{\mathrm{\partial }\phi }{\mathrm{\partial }z}\right)}$

${\displaystyle =\left(\frac{\mathrm{\partial }}{\mathrm{\partial }x},\frac{\mathrm{\partial }}{\mathrm{\partial }y},\frac{\mathrm{\partial }}{\mathrm{\partial }z}\right)\phi }$

,

${\displaystyle =\mathrm{\nabla }\phi }$

.

${\displaystyle \mathrm{d}\mathrm{i}\mathrm{v}\mathbf{A}=\frac{\mathrm{\partial }{A}_x}{\mathrm{\partial }x}+\frac{\mathrm{\partial }{A}_y}{\mathrm{\partial }y}+\frac{\mathrm{\partial }{A}_z}{\mathrm{\partial }z}}$

,

${\displaystyle =\left(\frac{\mathrm{\partial }}{\mathrm{\partial }x},\frac{\mathrm{\partial }}{\mathrm{\partial }y},\frac{\mathrm{\partial }}{\mathrm{\partial }z}\right)\cdot \mathbf{A}}$

,

${\displaystyle =\mathrm{\nabla }\cdot \mathbf{A}}$

.

${\displaystyle \mathrm{d}\mathrm{i}\mathrm{v}\mathrm{g}\mathrm{r}\mathrm{a}\mathrm{d}\phi =\mathrm{\nabla }\cdot (\mathrm{\nabla }\phi )}$

${\displaystyle =(\mathrm{\nabla }\cdot \mathrm{\nabla })\phi ={\mathrm{\nabla }}^2\phi =\mathrm{\Delta }\phi }$

,

${\displaystyle \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{l}\mathbf{A}=\left(\frac{\mathrm{\partial }{A}_z}{\mathrm{\partial }y}-\frac{\mathrm{\partial }{A}_y}{\mathrm{\partial }z},\frac{\mathrm{\partial }{A}_x}{\mathrm{\partial }z}-\frac{\mathrm{\partial }{A}_z}{\mathrm{\partial }x},\frac{\mathrm{\partial }{A}_y}{\mathrm{\partial }x}-\frac{\mathrm{\partial }{A}_x}{\mathrm{\partial }y}\right)}$

${\displaystyle f_x=\frac{df}{dx}}$

${\displaystyle f_{xx}=\frac{d^{2}f}{d{x}^2}.}$

${\displaystyle \frac{\mathrm{\partial }f}{\mathrm{\partial }x}=f_x={\mathrm{\partial }}_{x}f={\mathrm{\partial }}^{x}f,}$

• Earliest Uses of Symbols of Calculus, maintained by Jeff Miller.

• Mathematical Analysis I & II,V.A Zorich