Question

How do you find the derivative of `1 / (sinx+cosx)`?

Answer 1

`-1/sqrt(2)csc(x + pi/4) cot(x + pi/4)`

Explanation:

Done using an alternative approach

`(1 / (sinx+cosx))'`
`= ((1/sqrt(2)) / (sinx cos pi/4+cosx sin pi/4))'`
`= 1/sqrt(2)((1) / (sin(x + pi/4)))'`
`= 1/sqrt(2)(csc(x + pi/4))'`
`= -1/sqrt(2)csc(x + pi/4) cot(x + pi/4)`