Choosing a Differentiation Rule

The IB AA HL syllabus includes derivatives of \(\tan x\), \(\sec x\), \(\operatorname{cosec}x\), \(\cot x\), \(a^x\), \(\log_a x\), \(\arcsin x\), \(\arccos x\) and \(\arctan x\).

First identify the outer function. Apply its standard derivative, then use the chain rule for the inner expression. Use the product or quotient rule only when the whole expression is a product or quotient.

A first-principles calculation starts from \(f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}h\). For this course's examined first-principles questions, practise polynomial functions.

The formulae use radians for trigonometric derivatives. Check domains of logarithms, reciprocal functions and inverse circular functions before giving a derivative.