Question

How do you find the derivative of Inverse trig function `y = arc csc (x/2)`?

Answer 1

`2/ (x^2 sin x)`

Explanation:

`y=arc csc (x/2)`
`csc y = x/2`
`1/(cos y) = x/2`
`cos y = 2/x`

Diff wrt `x` on both sides:
`-sin y dy/dx = -2/x^2`
`dy/dx = 2/ (x^2 sin y)`
`d/dx arc csc (x/2) = 2/ (x^2 sin y)`