======derivace====== * [[cs>Derivace]] * [[wa>taylor series sin x]] ======součtu====== linearita derivace \( (af + bg)' = af' + bg' \) ======součinu====== \( (f g)' = f'g + fg' \) ======podílu====== \( (\frac{f}{g})' = \frac{f'g - fg'}{g^2} \) ======primitivních funkcí====== \( (\log_a x)' = \frac{1}{x \ln a} \) \( (\ln x)' = \frac{1}{x} \) [[wa> derivative a^x ]] \( a^x \ln a \) \( (\sin x )' = \cos x, (\cos x)' = - \sin x \) [[wa>csc x, sin x]], [[cs>Kosekans]] [[wa>sec x, cos x]] \( (\tan x)' = \frac{1}{cos^2 x} \) \( (\cot x)' = \frac{-1}{sin^2 x} \) \( \int \tan x dx = \ln \sin x \) [[wa>integrate tan x]] [[wa> d/dx tan(x) ]] [[wa> solve y'(x) = tan(x) ]] [[wa> series of int tan(x) dx ]] \( (a^x)' = a^x \ln a \), speciálně \( (e^x)' = e^x \) ======arcsin====== \( ( \arcsin x )' = \frac{1}{\sqrt{1 - x^2}} \) [[wa> derivative sin^-1 x]] \( ( \arccos x )' = -\frac{1}{\sqrt{1 - x^2}} \) [[wa> derivative cos^-1 x]] \( ( \arctan x )' = \frac{1}{{1 + x^2}} \) [[wa> derivative tan^-1 x]] [[wa> derivative cot^-1 x]] ======sinh====== \( ( \sinh x )' = \cosh x \), funkce vypadají takto: [[wa>plot sinh x, cosh x, 1/x]]