Recently, the q−derivative operator has been used to investigate several subclasses of analytic functions in different ways with different perspectives by many researchers and their interesting results are too voluminous to discuss. For example, the extension of the theory of univalent functions can be used to describe the theory of q−calculus, q−calculus operator are also used to construct several subclasses of analytic functions and so on. In this work, we considered the FeketeSzego problem for certain analytic functions defined by q−derivative operator with respect to symmetric and conjugate points. The early few coefficient bounds were obtained to derive our results.