微分 (derivative)

微分・勾配記号

出力$\TeX$
$\nabla$\nabla
$\partial$\partial

1次微分

$$ \dot x = x^{\prime} = dx/dt=\frac{d x(t)}{d t}=\frac{d}{d t}\left(x(t)\right), $$

2次微分

$$ \ddot x = x^{\prime \prime} = d^{2}x/dt^{2}=\frac{d^{2} x(t)}{d t^{2}}=\frac{d^{2}}{d t^{2}}\left(x(t)\right), $$

偏微分

$$ \frac{\partial f(x,y)}{\partial x} =\partial_{x}f(x,y)=f_{x}(x,y), $$

REFERENCES:

  • http://hooktail.sub.jp/nocategory/latexImpress/