Question

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

Answer 1

`= -pi csc pi x cot pi x`

Explanation:

`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`