Sin cos Tan must memorise. These are part of the syllabus.

(Actually, even Tan can be derived from sin or cos)

2nd line of the first one looks incorrect. Should be a^x /lna instead of a^x / lnx

You can actually derive all these from first principles.

But it is really too much of a hassle and it is better to memorise them so you can apply them quickly in the exam.

In the O Level A Math syllabus, students are not expected to derive such identities from first principles (i.e limits). These are usually reserved for mathematics courses at higher levels

cot, cosec(or csc, depends on how you abbreviate it) and sec can be derived from sin cos tan but it also wastes time in exam condition.

However, doing it in your free time would be good to have the actualisation/realisation of how these make sense.

I don’t think O Level candidates are expected to memorise cosec Sec and cot derivatives though. The syllabus outline mentions only for sin cos and Tan.

Not expected to, but it saves time should it come out in exam.

Anyway, students hardly ask about these 3 since they are expected to convert it to sin cos tan.

Derivatives of cosec x and sec x are found in MF26, so this student could be from an IP school (where they often teach ahead of O level syllabus, in preparation for A levels directly)

Oh yes. The a^x derivative isn't in O levels also.