Таблица основных производных

Функция Производная
\(C\) (константа) \(0\)
\(x^n\) \(nx^{n-1}\)
\(e^x\) \(e^x\)
\(a^x\) \(a^x \ln a\)
\(\ln x\) \(\frac{1}{x}\)
\(\log_a x\) \(\frac{1}{x \ln a}\)
\(\sin x\) \(\cos x\)
\(\cos x\) \(-\sin x\)
\(\tan x\) \(\frac{1}{\cos^2 x} = \sec^2 x\)
\(\cot x\) \(-\frac{1}{\sin^2 x} = -\csc^2 x\)
\(\arcsin x\) \(\frac{1}{\sqrt{1-x^2}}\)
\(\arccos x\) \(-\frac{1}{\sqrt{1-x^2}}\)
\(\arctan x\) \(\frac{1}{1+x^2}\)
\(\operatorname{arccot}x\) \(-\frac{1}{1+x^2}\)
\(\sinh x\) \(\cosh x\)
\(\cosh x\) \(\sinh x\)
\(\tanh x\) \(\operatorname{sech}^2 x\)
\(\coth x\) \(-\operatorname{csch}^2 x\)