Page 175 - ADVANCED MATH F.5

Form Five Form Five

Introduction to partial derivatives
Teaching steps

1. Introduce students through discussion to the concept of partial
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derivatives of a function z = f (, )xy where the two variables
x and y are independent of each other.
2. Guide students through discussion to identify functions of
two independent variables. Lead them to deduce the partial
derivative of z with respect to x and the partial derivative of z
with respect to y.
3. Assist students through discussion to recognize various
notations used for writing partial derivatives of functions.

4. Use Examples 8.76 to 8.79 in the Student’s Book to guide
students to apply partial derivatives to find solutions for the
given examples.
5. Assign students to attempt Exercise 8.19 in the Student’s
Book. Advise them to submit their work; check the correctness
of their answers, and provide them constructive feedback.

Answers to Exercise 8.19

p ∂ T p ∂ 1
1. = − k ; = k
∂ V V 2 ∂ T V

z ∂ z ∂
2
2
2. = 2xy 3 , = 3x y
x ∂ y ∂
z ∂ 1 2y z ∂ 2x 1
3. = + and = − −
x ∂ y 2 x 3 y ∂ y 3 x 2

3
cos xy
4. (a) 2 sinx ( ) 3xy + 3 x 2 ( y x + 2 4y 2 ) ( ) (b) x + 2 2xy − y 2
( x + ) y 2
(c) ( 63xy+ )

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