MAT2691 Mathematics II (Engineering) Assignment 01 Semester 2 2022.

MAT2691 Mathematics II (Engineering) Assignment 01 Semester 2 2022. Assignment 01 Semester 2 This assignment contributes 40% to your year mark. QUESTION 1 Determine dx dy of the following and simplify if possible.   3 2 2 3 2 3 2 2 2 2 3 1.1 implicit differentiation 3 2 1 2 1 3 1 3 2 x y xy x dy dy x y x y x y dx dx dy x xy x y y dx dy x y y dx x xy                              (5)       2 2 2 2 1.2 8 logarithmic differentiation (8 ) 1 8 2 (8 ) 8 8 2 (8 ) x x y x ny x n x dy x n x x y dx x dy x x n x x dx                 (5) 1.3 2 2 arctan 1 x y x                            2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 Put , then ' 1 1 2 2 4 1 2 1 1 x x x x f x f x x x x x x x x                                           2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 2 2 4 2 2 2 2 2 1 1 . 4 1 1 1 2 1 1 . 1 4 1 1 1 2 1 . 1 2 4 1 2 1 1 2 2 1 1 2 1 x dy dx x x x x x x x x x x x x x x x x x x x x                                                (5)