### Теория:

Формулами дифференцирования обычно называют формулы для нахождения производных конкретных функций, например:

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