  In this article we discuss an important students' misconception about
derivatives, that the expression of the derivative of the function contains the
information as to whether the function is differentiable or not where the
expression is undefined. As a working example we consider a typical Calculus
problem of finding the horizontal tangent lines of a function. Following the
standard procedure, we derive the expression for the derivative using Product
Rule. The search for the values of the independent variable, that make the
derivative equal zero, leads to missing the unique solution of the problem. We
show that in this case, even though the expression of the derivative is
undefined, the function indeed possesses the derivative at the point. We also
provide the methodological treatment of such functions, which can be
effectively used in the classroom.
