Common Mistakes in differentiation and trigonometry (1 Viewer)

[StarKiller2196]

What are some common mistakes people make on questions such as:
differentiation
Auxiliary Angle questions
Derivative Graphing
Thanks

 

[Pedro123]

Differentiation - Usually nothing, but if you don't have the identities down pat, then it can be annoying (i.e. sec(x), cot(x), inverse functions, etc)
Auxiliary Angle - Not remembering all the different formulas (Many people only remember a few since some can be derived, however in an exam it is much better if you remember everything). Also t substitution can be annoying
Derivative graphing - this is mostly just stupid misinterpretation issues, i.e. not realising when a curve has a reducing derivative that is still positive, points of inflextion

 

[fan96]

This is one of the more common differentiation mistakes.



For trigonometry in general, people make a lot of mistakes.



, or equivalently,

A lot of these involve division by zero.



Many such examples are nuanced.
One example discussed here recently was the CSSA 2019 trial paper, where one of the questions was



This equality is not even true to begin with, for reasons discussed in that thread.

The take-away here is that you should never divide by anything unless you know that it will never be zero.

 

[CM_Tutor]

Mistakes can be made with auxilliary angle method questions by not adjusting the domain (or doing so incorrectly), and thereby losing solutions