نمادگذاری‌های مشتق

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

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

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

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

${\displaystyle =\nabla \varphi }$ .

${\displaystyle \mathrm {div\,} \mathbf {A} ={\partial A_{x} \over \partial x}+{\partial A_{y} \over \partial y}+{\partial A_{z} \over \partial z}}$ ,

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

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

${\displaystyle \mathrm {div} \,\mathrm {grad} \,\varphi \,=\nabla \cdot (\nabla \varphi )}$

${\displaystyle =(\nabla \cdot \nabla )\varphi =\nabla ^{2}\varphi =\Delta \varphi }$ ,

${\displaystyle \mathrm {curl} \,\mathbf {A} =\left({\partial A_{z} \over {\partial y}}-{\partial A_{y} \over {\partial z}},{\partial A_{x} \over {\partial z}}-{\partial A_{z} \over {\partial x}},{\partial A_{y} \over {\partial x}}-{\partial A_{x} \over {\partial y}}\right)}$

${\displaystyle f_{x}={\frac {df}{dx}}}$

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

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

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

• Mathematical Analysis I & II,V.A Zorich