A-level Mathematics/MEI/FP2/Advanced Calculus

This chapter assumes you have a good knowledge of several techniques you should have learned in Core Mathematics, notably the product, quotient and chain rules for differentiation, integration by substitution and parts and an awareness of trigonometric identities including double angle formulas.

You are given the following standard results in the MEI formula booklet:

${\displaystyle f(x)}$	${\displaystyle f'(x)}$
${\displaystyle y=\arcsin x}$	${\displaystyle {\frac {1}{\sqrt {1-x^{2}}}}}$
${\displaystyle y=\arccos x}$	${\displaystyle {\frac {-1}{\sqrt {1-x^{2}}}}}$
${\displaystyle y=\arctan x}$	${\displaystyle {\frac {1}{1+x^{2}}}}$

${\displaystyle f(x)}$	${\displaystyle \int f(x)dx}$ (+ a constant)
${\displaystyle {\frac {1}{\sqrt {a^{2}-x^{2}}}}}$	${\displaystyle \arcsin \left({\frac {x}{a}}\right)}$
${\displaystyle {\frac {1}{a^{2}+x^{2}}}}$	${\displaystyle {\frac {1}{a}}\arctan \left({\frac {x}{a}}\right)}$

The best way to show how to use these is with a few examples: