Nevezetes függvények deriváltjai

\( (c)'=0 \quad \left( x^n \right)' = n x^{n-1} \quad \left( e^x \right)' = e^x \quad \left( a^x \right)' = a^x \ln{a} \)

\( ( \ln{x} )' = \frac{1}{x} \quad ( \log_a{x} )' = \frac{1}{x} \frac{1}{\ln{a}} \quad ( \sin{x} )' = \cos{x} \quad ( \cos{x} )' = - \sin{x} \)

\( ( \tan{x} )' = \frac{1}{\cos^2{x} } \quad ( \arcsin{x} )' = \frac{1}{\sqrt{1-x^2}} \quad ( \arccos{x} )' = \frac{-1}{\sqrt{1-x^2}} \quad (\arctan{x})' = \frac{1}{1+x^2} \)