If `f(x)=|x^nn !2cosxcos(npi)/2 4sinxsin(npi)/2 8|` then find the value of `(d^n)/(dx^n)([f(x)])_(x=0)dot(n in z)dot`

Explanation

` (d^n)/(dx^n)[f(x)]= |{:( (d^(n))/(dx^(n))(x^(n)),,n!,,2),((d^(n))/(dx^(n))(cos x),,cos.(npi)/(2),,4),((d^(n))/(dx^(n)) (sinx),,sin .(npi)/(2),,8):}|`
`=|{:(n!,,n!,,2),(cos (x+(npi)/(2)),,cos .(npi)/(2),,4),(sin (x+(npi)/(2)),,sin .(npi)/(2),,8):}|( n in Z)`
`rArr (d^(n))/(dx^(n)) [f(x)]_(x=0) =0" "(:' C_(1) " and " C_(2) " are same)"`