f' represents the derivative of a function f of one argument.
Derivative[n1, n2, ...][f] is the general form, representing a function obtained from f by differentiating n1 times with respect to the first argument, n2 times with respect to the second argument, and so on.
You can think of Derivative as a functional operator which acts on functions to give derivative functions.
Derivative is generated when you apply D to functions whose derivatives Mathematica does not know.
Mathematica attempts to convert Derivative[n][f] and so on to pure functions. Whenever Derivative[n][f] is generated, Mathematica rewrites it as D[f[#], {#, n}]&. If Mathematica finds an explicit value for this derivative, it returns this value. Otherwise, it returns the original Derivative form.
Derivative[-n][f] represents the n indefinite integral of f.
Derivative[{n1, n2, ...}][f] represents the derivative of f[{x1, x2, ...}] taken ni times with respect to xi. In general, arguments given in lists in f can be handled by using a corresponding list structure in Derivative.
N[f'[x]] will give a numerical approximation to a derivative.
indefinite integral of f. 
EXAMPLES
Basic Examples 
Scope 