### Теорія:

Формулами диференціювання зазвичай називають формули для знаходження похідних конкретних функцій, наприклад:

 $\begin{array}{l}\phantom{\rule{0.147em}{0ex}}\left(C\right)\mathrm{\prime }=0,\phantom{\rule{0.147em}{0ex}}\text{де}\phantom{\rule{0.147em}{0ex}}C\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}\text{постійна величина}\\ {x}^{\prime }=1\\ {\left(\mathit{kx}+m\right)}^{\prime }=k\\ {\left({x}^{2}\right)}^{\prime }=2x\\ {\left(\frac{1}{x}\right)}^{\prime }=-\frac{1}{{x}^{2}}\\ {\left(\sqrt{x}\right)}^{\prime }=\frac{1}{2\sqrt{x}}\\ \phantom{\rule{0.147em}{0ex}}\left({x}^{a}\right)\mathrm{\prime }=a{x}^{a-1}\phantom{\rule{0.147em}{0ex}}\\ \phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\left({e}^{x}\right)\mathrm{\prime }={e}^{x}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\\ \phantom{\rule{0.147em}{0ex}}\left(\mathit{sin}\phantom{\rule{0.147em}{0ex}}x\right)\mathrm{\prime }=\mathit{cos}\phantom{\rule{0.147em}{0ex}}x\phantom{\rule{0.147em}{0ex}}\\ \left(\mathit{cos}\phantom{\rule{0.147em}{0ex}}x\right)\mathrm{\prime }=-\mathit{sin}\phantom{\rule{0.147em}{0ex}}x\phantom{\rule{0.147em}{0ex}}\\ \phantom{\rule{0.147em}{0ex}}\left(\mathit{tg}\phantom{\rule{0.147em}{0ex}}x\right)\mathrm{\prime }=\frac{1}{{\mathit{cos}}^{2}x}\phantom{\rule{0.147em}{0ex}}\\ \phantom{\rule{0.147em}{0ex}}\left(\mathit{ctg}\phantom{\rule{0.147em}{0ex}}x\right)\mathrm{\prime }=-\frac{1}{{\mathit{sin}}^{2}x}\phantom{\rule{0.147em}{0ex}}\\ \phantom{\rule{0.147em}{0ex}}\left(\mathit{arcsin}\phantom{\rule{0.147em}{0ex}}x\right)\mathrm{\prime }=\frac{1}{\sqrt{1-{x}^{2}}}\phantom{\rule{0.147em}{0ex}}\\ \phantom{\rule{0.147em}{0ex}}\left(\mathit{arccos}\phantom{\rule{0.147em}{0ex}}x\right)\mathrm{\prime }=-\frac{1}{\sqrt{1-{x}^{2}}}\phantom{\rule{0.147em}{0ex}}\\ \phantom{\rule{0.147em}{0ex}}\left(\mathit{arctg}\phantom{\rule{0.147em}{0ex}}x\right)\mathrm{\prime }=\frac{1}{1+{x}^{2}}\phantom{\rule{0.147em}{0ex}}\\ \phantom{\rule{0.147em}{0ex}}\left(\mathit{arcctg}\phantom{\rule{0.147em}{0ex}}x\right)\mathrm{\prime }=-\frac{1}{1+{x}^{2}}\phantom{\rule{0.147em}{0ex}}\end{array}$
Джерела: