if a question ask us to differentiate cosecx, secx or cotx, we can just convert it to their trigo ratios like 1/sinx, 1/cosx or cosx/sinx, it is not necessary to follow the differentiation rule of converting secx to secxtanx, cotx to - cosecx etc?

how about a question that ask us to differentiate cosec^2x, sec^2x and cot^2x tho

if a question ask us to differentiate cosecx, secx or cotx, we can just convert it to their trigo ratios like 1/sinx, 1/cosx or cosx/sinx, it is not necessary to follow the differentiation rule of converting secx to secxtanx, cotx to - cosecx etc?

how about a question that ask us to differentiate cosec^2x, sec^2x and cot^2x tho

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At your level, the proper way is to convert it to sin, cos or tan before proceeding. Only students who proceed to JC or some poly courses will see the derivative of cosec, sec and cot directly (which of course can be easily found even in the O Levels). So in short, you can use the "rule", though you do not actually need to memorise it.

Anyway, cot x differentiates to - cosec² x.

To differentiate cosec² x, we can easily rewrite this as (sin x) ^ -2 and then do the usual bring down power and chain. Similar idea applies for sec² x, cot² x and higher powers.

thx :)

I just received your text, wonder why there has been no notifications for the past few days on all incoming texts

for 3d the answer in my textbook is 32/x^2(cosec^5(8/x)cos(8/x)) tho...