With both scalar and vector functions concerning a vector variable, the first order partial derivatives are defined. Any way the new aspects on first order partial derivative of fuzzy matrix functions based on a vector variable in the compatible norm is also still limited. The initial step in this paper's presentation is a systematic generalization of the definitions of first order partial derivatives of scalar functions, vector functions, and fuzzy matrix functions on the basis of a vector variable. A brief introduction to matrix calculus is followed by the presentation of the quadratic form. However, I shall be working with a symmetric fuzzy matrix with a compatible norm in this instance.