class_docstr: Represents the limiting behavior of some function.
  
  Explanation
  ===========
  
  The order of a function characterizes the function based on the limiting
  behavior of the function as it goes to some limit. Only taking the limit
  point to be a number is currently supported. This is expressed in
  big O notation [1]_.
  
  The formal definition for the order of a function `g(x)` about a point `a`
  is such that `g(x) = O(f(x))` as `x \rightarrow a` if and only if there
  exists a `\delta > 0` and an `M > 0` such that `|g(x)| \leq M|f(x)|` for
  `|x-a| < \delta`.  This is equivalent to `\limsup_{x \rightarrow a}
  |g(x)/f(x)| < \infty`.
  
  Let's illustrate it on the following example by taking the expansion of
  `\sin(x)` about 0:
  
  .. math ::
      \sin(x) = x - x^3/3! + O(x^5)
  
  where in this case `O(x^5) = x^5/5! - x^7/7! + \cdots`. By the definition
  of `O`, there is a `\delta > 0` and an `M` such that:
  
  .. math ::
      |x^5/5! - x^7/7! + ....| <= M|x^5| \text{ for } |x| < \delta
  
  or by the alternate definition:
  
  .. math ::
      \lim_{x \rightarrow 0} | (x^5/5! - x^7/7! + ....) / x^5| < \infty
  
  which surely is true, because
  
  .. math ::
      \lim_{x \rightarrow 0} | (x^5/5! - x^7/7! + ....) / x^5| = 1/5!
  
  
  As it is usually used, the order of a function can be intuitively thought
  of representing all terms of powers greater than the one specified. For
  example, `O(x^3)` corresponds to any terms proportional to `x^3,
  x^4,\ldots` and any higher power. For a polynomial, this leaves terms
  proportional to `x^2`, `x` and constants.
  
  Examples
  ========
  
  >>> from sympy import O, oo, cos, pi
  >>> from sympy.abc import x, y
  
  >>> O(x + x**2)
  O(x)
  >>> O(x + x**2, (x, 0))
  O(x)
  >>> O(x + x**2, (x, oo))
  O(x**2, (x, oo))
  
  >>> O(1 + x*y)
  O(1, x, y)
  >>> O(1 + x*y, (x, 0), (y, 0))
  O(1, x, y)
  >>> O(1 + x*y, (x, oo), (y, oo))
  O(x*y, (x, oo), (y, oo))
  
  >>> O(1) in O(1, x)
  True
  >>> O(1, x) in O(1)
  False
  >>> O(x) in O(1, x)
  True
  >>> O(x**2) in O(x)
  True
  
  >>> O(x)*x
  O(x**2)
  >>> O(x) - O(x)
  O(x)
  >>> O(cos(x))
  O(1)
  >>> O(cos(x), (x, pi/2))
  O(x - pi/2, (x, pi/2))
  
  References
  ==========
  
  .. [1] `Big O notation <https://en.wikipedia.org/wiki/Big_O_notation>`_
  
  Notes
  =====
  
  In ``O(f(x), x)`` the expression ``f(x)`` is assumed to have a leading
  term.  ``O(f(x), x)`` is automatically transformed to
  ``O(f(x).as_leading_term(x),x)``.
  
      ``O(expr*f(x), x)`` is ``O(f(x), x)``
  
      ``O(expr, x)`` is ``O(1)``
  
      ``O(0, x)`` is 0.
  
  Multivariate O is also supported:
  
      ``O(f(x, y), x, y)`` is transformed to
      ``O(f(x, y).as_leading_term(x,y).as_leading_term(y), x, y)``
  
  In the multivariate case, it is assumed the limits w.r.t. the various
  symbols commute.
  
  If no symbols are passed then all symbols in the expression are used
  and the limit point is assumed to be zero.
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code: def _eval_derivative(self, x):
      return self.func(self.expr.diff(x), *self.args[1:]) or self
  
imports: from sympy.core import S, sympify, Expr, Dummy, Add, Mul
  from sympy.core.cache import cacheit
  from sympy.core.containers import Tuple
  from sympy.core.function import Function, PoleError, expand_power_base, expand_log
  from sympy.core.sorting import default_sort_key
  from sympy.functions.elementary.exponential import exp, log
  from sympy.sets.sets import Complement
  from sympy.utilities.iterables import uniq, is_sequence
label_desc: Use image node_id 15 for calling the Order obj's underlying member method code with example usage: obj._eval_derivative(x) and returns: unknown