Math post
08/02/25 00:39
呢題曾經post過，
今次用LibreOffice Writer執番靚仔：
08/02/25 00:54
呢題中二程度
08/02/25 00:56
呢題中二程度
Proofread version:
08/02/25 01:22
Enrichment question with unproofread solution:
08/02/25 01:56
跟住呢題同HKDSE M2被廢除嘅微分部分有關：
dx/dy = 1/(dy/dx)
Questions:
(a) Find d ln(x) /dx
(b) Find d x^(1/3) / dx
08/02/25 02:02
跟住呢題同HKDSE M2被廢除嘅微分部分有關：
dx/dy = 1/(dy/dx)
Questions:
(a) Find d ln(x) /dx
(b) Find d x^(1/3) / dx
Solution:
(a) Recall d e^x /dx = e^x
Now d lnx /dx = d lnx/d e^(ln x)
= 1/ [e^(ln x)] = 1/x
(b) Recall d x^3 /dx = 3 x^2
Now d x^(1/3) /dx = d x^(1/3)/d ((x^3)^(1/3))
= 1/ [3 (x^(1/3))^2] = 1/ (3 x^(2/3)) = x^(-2/3) /3