Математика

Производные простейших функций:

${\left(c\right)}^{\text{'}}=0$

${\left(x^a\right)}^{\text{'}}=a{x}^{a-1}$

${\left(a^x\right)}^{\text{'}}=a^x\ln a$

${\left({\log }_{a}x\right)}^{\text{'}}=\frac{1}{x\ln a}$

Производные тригонометрических функций:

${\left(\sin x\right)}^{\text{'}}=\cos x$

${\left(\cos x\right)}^{\text{'}}=-\sin x$

${\left(\mathrm{tg}x\right)}^{\text{'}}=\frac{1}{{\cos }^{2}x}$

${\left(\mathrm{ctg}x\right)}^{\text{'}}=-\frac{1}{{\sin }^{2}x}$

Правила дифференцирования:

$C^{\text{'}}=0$

$x^{\text{'}}=1$

${\left(f+g\right)}^{\text{'}}=f^{\text{'}}+g^{\text{'}}$

${\left(\mathit{fg}\right)}^{\text{'}}=f^{\text{'}}g+f{g}^{\text{'}}$

${\left(\mathit{Cf}\right)}^{\text{'}}=C{f}^{\text{'}}$

${\left(\frac{f}{g}\right)}^{\text{'}}=\frac{f^{\text{'}}g-f{g}^{\text{'}}}{g^2}$

Производная сложной функции:

$h^{\text{'}}\left(x_0\right)=g\text{'}\left(f\left(x_0\right)\right)\cdot f\text{'}\left(x_0\right)$