Page 168 - ADVANCED MATH F.5

Form Five Form Five

The second derivative of a function

Teaching steps
1. Guide students through discussions to find the second derivative
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of a function. Assist them through discussion to write the
second derivative of a function using various notations.
2. Use Examples 8.50 to 8.51 in the Student’s Book to guide
students and assist them to find the second derivative of a
function. Engage students to verify the solution by using a
mathematical software of your choice.

3. Introduce students through discussion to recognize parametric
functions. Guide students to deduce derivatives of parametric
functions using the chain rule.

4. Use Examples 8.52, 8.53, and 8.54 in the Student’s Book to
guide students and assist them to find derivatives of parametric
functions. Engage students to verify the solutions by using a
mathematical software of their choice.
5. Assign students to attempt Exercise 8.13 in the Student’s Book.
Advise students to submit their work; check the correctness of
their answers, and provide them constructive feedback.

Answers to Exercise 8.13

4 cosxcosx
d y ( 6 x−
dy
2 2
2sin xsin x
2. dy = = xc x cos x −os x − 2 ; ; d y = = ( 6 x− 2 2 ) sin x − ) sin x − 4 x x
dx x x 3 3 dx 2 2 x x 4 4
dx
dx
2
dy (2t + ) 1 2 dy − ( 22t + ) 1 3
3. (a) = (b) =
dx t 2 dx 2 3t 3
2
dy 9
(c) =
dx 2 4
162
Mathematics for Advanced Secondary Schools

30/06/2024 18:02:41
ADVANCED MATH F.5 TG CHAPTERS.indd 162
ADVANCED MATH F.5 TG CHAPTERS.indd 162 30/06/2024 18:02:41