MAT2691 Assignment 1 2022

MAT2691
Assignment 01
Semester 2
2022.

, Assignment 01 Semester 2


This assignment contributes 40% to your year mark.

QUESTION 1
dy
Determine of the following and simplify if possible.
dx

1.1 x 3y  xy 2 x implicit differentiation
 2 3 dy   2  dy  
 3x y  x    y  x  2 y   1
 dx    dx  
dy 3
dx
 x  2 xy   1 3x 2y  y 2

dy 1  3x 2y  y 2

dx x 3  2 xy (5)
x2
1.2 y  8 x  logarithmic differentiation
ny  x 2 n(8x)
1 dy  8  (5)
 2 x n (8 x)  x 2  
y dx  8x 
dy x2
 8 x   2 x n (8 x)  x 
dx
 2x 
1.3 y  arctan  2 
1 x 

Put f  x  
2x
, then f '  x  
1  x 2   2    2 x  2 x 
1  x2
1  x 2 
2


2  2 x2  4 x2

1  x 2 
2


2 1  x 2 

1  x 2 
2