Функция	Производная
\[c\]	\[0\]
\[x^{a}\]	\[ax^{a-1}\]
\[a^{x}\]	\[a^{x}\ln{(a)}\]
\[\log_a{x}\]	\[\frac{1}{x\ln{(a)}}\]

Функция	Производная
\[sin(x)\]	\[cos(x)\]
\[cos(x)\]	\[-sin(x)\]
\[tg(x)\]	\[\frac{1}{cos^2(x)}\]
\[ctg{(x)}\]	\[-\frac{1}{sin^2(x)}\]

Функция	Производная
\[arcsin(x)\]	\[\frac{1}{\sqrt{1-x^2}}\]
\[arccos(x)\]	\[-\frac{1}{\sqrt{1-x^2}}\]
\[arctg(x)\]	\[\frac{1}{1+x^2}\]
\[arcctg(x)\]	\[-\frac{1}{1+x^2}\]

Действие	Равенство
\[(u\pm v)\\'\]	\[u\\'\pm v\\'\]
\[(uv)\\'\]	\[u\\'v+uv\\'\]
\[(\frac{u}{v})\\'\]	\[\frac{u\\'v-uv\\'}{v^2}\]
\[(u(v))\\'\]	\[u\\'(v)v\\'\]

Функция	Производная
\[sh(x)\]	\[ch(x)\]
\[ch(x)\]	\[sh(x)\]
\[th(x)\]	\[\frac{1}{ch^2(x)}\]
\[cth(x)\]	\[-\frac{1}{sh^2(x)}\]

Функция	Производная
\[arsh(x)\]	\[\frac{1}{\sqrt{x^2+1}}\]
\[arch(x)\]	\[\frac{1}{\sqrt{x^2-1}}\]
\[arth(x)\]	\[\frac{1}{1-x^2}\]
\[arcth(x)\]	\[\frac{1}{1-x^2}\]