derivace
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
\( (\log_a x)' = \frac{1}{x \ln a} \)
\( (\ln x)' = \frac{1}{x} \)
derivative a^x \( a^x \ln a \)
\( (\sin x )' = \cos x, (\cos x)' = - \sin x \)
csc x, sin x, Kosekans sec x, cos x
\( (\tan x)' = \frac{1}{cos^2 x} \) \( (\cot x)' = \frac{-1}{sin^2 x} \)
\( \int \tan x dx = \ln \sin x \) integrate tan x d/dx tan(x) solve y'(x) = tan(x) series of int tan(x) dx
\( (a^x)' = a^x \ln a \), speciálně \( (e^x)' = e^x \)
arcsin
\( ( \arcsin x )' = \frac{1}{\sqrt{1 - x^2}} \) derivative sin^-1 x
\( ( \arccos x )' = -\frac{1}{\sqrt{1 - x^2}} \) derivative cos^-1 x
\( ( \arctan x )' = \frac{1}{{1 + x^2}} \) derivative tan^-1 x derivative cot^-1 x
sinh
\( ( \sinh x )' = \cosh x \), funkce vypadají takto: plot sinh x, cosh x, 1/x
