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