Abstract: By letting the function f（x1‚x2‚…‚xn）have continuous partial derivatives of second order with respect to xn‚the functional equation ∑ n i＝1 （－1） i－1［ f （ x1‚…‚xi ＋ xi＋1‚…‚x n＋1）＋ f （ x1‚…‚xi － xi＋1‚…‚x n＋1）］ ＋ （－1） n2f （ x1‚x2‚…‚ x n） ＝0is considered．First‚the general solution of the equation ∑ n i＝1 （－1） i－1［ F（ x1‚…‚xi ＋ xi＋1‚…‚x n＋1）＋ F（ x1‚…‚xi － xi＋1‚…‚x n＋1）］ ＝0 was presented．Then‚the first functional equation was twice differentiated with respect to xn＋1 and reduced to an equation of the aforementioned type．It is found that the general solution of the first functional equation is f （ x1‚x2‚…‚x n） ＝ ∑ n－1 i＝1 （－1） i－1［ A（ x1‚…‚xi ＋ xi＋1‚…‚x n）＋ A （ x1‚…‚xi － xi＋1‚…‚x n）］ ＋ （－1） n－12A （ x1‚x2‚…‚x n－1） ． Where A（x1‚x2‚… xn－1）is an arbitrary twice continuous differentiable with respect to xn－1．

Key words: functional equation, differentiable solution, partial derivative