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Solution: y(x) = 1 (x) nR f(˘) (˘)d˘+ C Exact 0 = M(x;y)dx+ N(x;y)dy Solution: u(x;y) = const where Form the Fundamental Matrix Solution: = v 11e 1 tv 21e 2 v 12e 1t v 22e 2t the rst-order partial derivatives of f: rf(x) = ¶f(x) ¶x = 0 B B @ ¶y ¶x 1 ¶y ¶x n 1 C C A De nition: Hessian TheHessian matrix, or simply theHessian, denoted H, is an n n matrix containing the second derivatives of f: H = 0 B B B @ ¶2y ¶x2 1 ¶ 2y ¶x 1 n. the derivative of the (n-1) derivative, fx(n-1 The dot product remains in the formula and we have to construct the “vector by vector” derivative matrices. Suppose that we have a matrix Y = [y ij ] whose This document provides a summary of matrix and vector derivatives. Derivatives Cheat Sheet. Course. Some properties of orthogonal U and V: Columns are orthonormal: uT i j = ij. 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