Introductory calculus classes at the college level are often used as "gatekeepers" or "filters" for science and engineering majors. However, some researchers have questioned whether calculus courses, as currently taught, are filtering students appropriately (Black & Hernandez-Martinez, 2016; Williams, 2012; Williams & Choudry, 2016). As such, there is a concern that students are not being adequately screened or prepared by most calculus classes. Central to introductory calculus classes is the derivative (Kidron, 2019). Scholars have discussed the ways in which representations of the derivative differ between disciplines (Dray et al., 2019), but there has been no formal research investigating the representations of the derivative valued by teachers of calculus and teachers of subsequent non-mathematics classes. This study, through a new survey instrument, determined there are significant differences between the representations of the derivative valued by various post-secondary teachers of both mathematics and STEM courses that have calculus as a pre- or corequisite. By analyzing these differences, recommendations can be made to improve calculus as a gateway course for non-mathematics majors. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]