A novel methodology is presented for performing sensitivity analyses of assembled plate structures using the Boundary Element Method (BEM). The main novelty of this work is that the exact implicit derivatives of the BEM formulations for assembled plate structures have been derived for the first time and incorporated into a newly developed Implicit Differentiation Method (IDM), enabling sensitivity analyses to be conducted for more complex and realistic structures in a more accurate, robust, and efficient manner than previous approaches. Three numerical examples are investigated to validate the derived exact implicit derivatives and to demonstrate how they could be used for a potential application involving the shape optimisation of a complex X-core structure from the canard of a Eurofighter Typhoon fighter jet. Results show that the newly developed IDM is more accurate, robust, and efficient when compared to alternative methodologies using derivatives obtained from methods such as the Finite Difference Method (FDM) and the Finite Element Method (FEM).