This document is a workshop presentation on partial differentiation. It provides the partial derivatives of the function f(x,y) = 5x^3 - 4x^2y + 3y^2. The specific partial derivatives calculated are: i) fx = 15x^2 - 8xy^3 ii) fy = 12x^2y - 6y iii) fxx = 30x - 8y^3 iv) fyy = 24x^2 - 6 v) fyx = 24xy^2 vi) fxy = 24xy^2

1. BBMP 1103
Mathematic Management
Exam Preparation Workshop Sept 2011
Part 6 - Partial Differentiation
Presented By: Dr Richard Ng
26 Nov 2011
2ptg – 4ptg

2. 6. Focus on Partial Differentiation
Question: 14 (May 2010)
Solve the following questions using partial differentiation:
a) Given a function f ( x, y) 5x 3 4 x 2 y 3 3 y 2
Find i) f x ( x, y ) iv) f yy ( x, y)
ii) f y ( x, y ) v) f yx ( x, y)
iii) f xx ( x, y) vi) f xy ( x, y)
Prepared by Dr Richard Ng (2011) Page 2

3. Suggested Answers:
f ( x, y) 5x 3 4 x 2 y 3 3y 2
i) f x 15x 2 (4 y 3 )[2 x]
15x 2 8xy3
ii) f y ( 4x 2 )[3 y 2 ] 6 y
12x 2 y 2 6 y
iii) f x 15x 2 8xy 3
f xx 30x (8 y 3 )[1]
f xx 30x 8 y 3
Prepared by Dr Richard Ng (2011) Page 3

4. iv) fy 12x 2 y 2 6 y
f yy ( 12x 2 )[2 y] 6
f yy 24x 2 y 6
v) fy 12x 2 y 2 6 y
f yx ( 12y 2 )[2x]
f yx 24xy 2
Prepared by Dr Richard Ng (2011) Page 4

5. vi) fx 15x 2 8xy 3
f xy ( 8x)[3 y 2 ]
f xy 24xy 2
Prepared by Dr Richard Ng (2011) Page 5

6. End of
Part 6