How do you differentiate $(sec(πx))/(tan(πx))$ ?

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Answer 1 · 2016-08-28T09:30:50

$= -pi csc pi x cot pi x$

$d/dx (sec(πx))/(tan(πx))$

$=d/dx (cos pi x)/(cos pi x sin pi x)$

$=d/dx ( sin pi x)^(-1) [= d/dx csc pi x]$

by power and chain rules
$= -( sin pi x)^(-2) * cos pi x * pi$

$= -(pi cos pi x)/( sin^2 pi x)$

$= -pi csc pi x cot pi x$

How do you differentiate (sec(πx))/(tan(πx)) (sec(πx))/(tan(πx))?