Dwyer (1967) provided extensive formulas for matrix derivatives, many of which are for derivatives with respect to symmetric matrices. The results of his article are only for symmetric matrices whose (j, i) element is considered to differ from the (i, j) element even though their scalar values are equal. A simple result is given that extends the use of Dwyer's formulas to symmetric matrices in which the (i, j) element is considered functionally equal to the (j, i) element. Application of the results are illustrated by deriving the multivariate normal information matrix.