differentiate with respect to x to the given function`(x^(2)cospi/4)/(sinx)`

Explanation

`y=(x^(2)cospi/4)/(sinx) = (x^(2)/sqrt(2))/(sinx)`
`y=1/sqrt(2).x^(2)/(sinx)`
`(dy)/(dx) = 1/sqrt(2)[(sinx.d/(dx)(x^(2)-x^(2)d/(dx)sinx))/(sin^(2)x)]` [by quotient rule]
`=1/sqrt(2)[(sin2x-x^(2).cosx)/(sin^(2)x)]`
`=1/sqrt(2)(2xsinx-x^(2)cosx)/(sin^(2)x)]`
`=1/sqrt(2)[2"cosec"x-xcotx"cosec"x]`
`=x/sqrt(2)"cosec"[2-xcotx]`