Производная логарифма с основанием a

\[f(x) = \log_a{x} \]

\[ f^\prime (x) = \frac{1}{x \ln{a}}\]

\[f(x) = x^n \]

\[ f^\prime (x) = n x^{n-1}\]

\[f(x) = C \]

\[ f^\prime (x) = 0\]

\[f(x) = e^x \]

\[ f^\prime (x) = e^x\]

\[f(x) = \sin{x} \]

\[ f^\prime (x) = \cos{x}\]

\[f(x) = \cos{x} \]

\[ f^\prime (x) = - \sin{x}\]

\[f(x) = \mathrm{tg}{x} \]

\[ f^\prime (x) = \frac{1}{\cos^2{x}}\]

\[f(x) = \mathrm{ctg}{x} \]

\[ f^\prime (x) = \frac{-1}{\sin^2{x}}\]

\[f(x) = \ln{x} \]

\[ f^\prime (x) = \frac{1}{x}\]

\[f(x) = \arcsin{x} \]

\[ f^\prime (x) = \frac{1}{\sqrt{1-x^2}}\]

\[f(x) = \arccos{x} \]

\[ f^\prime (x) = \frac{-1}{\sqrt{1-x^2}}\]

\[f(x) = \mathrm{arctg}{x} \]

\[ f^\prime (x) = \frac{1}{1 + x^2}\]

\[f(x) = \mathrm{arcctg}{x} \]

\[ f^\prime (x) = \frac{-1}{1 + x^2}\]

\[f(x) = a^x \]

\[ f^\prime (x) = a^x \ln{a}\]