Book:L. Harwood Clarke/A Note Book in Pure Mathematics/Errata

Errata for 1953: L. Harwood Clarke: A Note Book in Pure Mathematics

Derivative of $\paren {x - 2}^{1/3} \paren {x - 3}^{1/2} \paren {2 x - 1}^{3/2}$

$\text {II}$. Calculus: Differentiation: Variable Index: Example

Let $y = \paren {x - 2}^{1/3} \paren {x - 3}^{1/2} \paren {2 x - 1}^{3/2}$,

then $\dfrac {\d y} {\d x} = \paren {\dfrac 1 {3 \paren {x - 2} } + \dfrac 1 {2 \paren {x - 3} } + \dfrac 3 {2 x - 1} } \paren {x - 1}^{1/3} \paren {x - 3}^{1/2} \paren {2 x - 1}^{3/2}$

Primitive of Function under its Derivative

$\text {II}$. Calculus: Integration

$\ds \int \frac {\map {f'} x} {\map f x} \rd x = \map \ln {\map f x}$

Sum of Arctangents

$\text V$. Trigonometry: Formulae $(39)$

$\tan^{-1} a + \tan^{-1} b = \tan^{-1} \dfrac {a + b} {1 - a b}$

Difference of Arctangents

$\text V$. Trigonometry: Formulae $(40)$

$\tan^{-1} a - \tan^{-1} b = \tan^{-1} \dfrac {a - b} {1 + a b}$