Definition:Elementary Function

An elementary function is one of the following:


 * The constant function: $$f_c \left({x}\right) = c$$ where $$c \in \R$$;


 * Powers of $$x$$: $$f \left({x}\right) = x^y$$, where $$y \in \R$$;


 * Exponentials: $$f \left({x}\right) = e^x$$;


 * Natural logarithms: $$f \left({x}\right) = \ln x$$;


 * Trigonometric functions: $$f \left({x}\right) = \sin x$$, $$f \left({x}\right) = \cos x$$;


 * Inverse trigonometric functions: $$f \left({x}\right) = \arcsin x, f \left({x}\right) = \arccos x$$;


 * All functions obtained by replacing $$x$$ with any of the functions above, e.g. $$f \left({x}\right) = \ln \sin x, f \left({x}\right) = e^{\cos x}$$;


 * All functions obtained by adding, subtracting, multiplying and dividing any of the above types any finite number of times.