If ` f(x)=|(x^n,n!,2),(cosx,cos((npi)/2),4),(sinx,sin((npi)/2),8)|`, then find the value of `d^n/(dx^n)[f(x)]_(x=0)`

if =|{:(x^(n),,n!,,2),(cos x,,cos.(npi)/(2),,4),(sin x,,sin .(npi)/(2),,8):}|, then find the value of (d^(n))/(dx^(n)) [f(x)]_(x=0) .(n in z).

if = |{:(x^(n),,n!,,2),(cos x,,cos.(npi)/(2),,4),(sin x,,sin .(npi)/(2),,8):}|, then find the value of (d^(n))/(dx^(n)) [f(x)]_(x=0) .(n in z) .

if =|{:(x^(n),,n!,,2),(cos x,,cos.(npi)/(2),,4),(sin x,,sin .(npi)/(2),,8):}|, then find the value of (d^(n))/(dx^(n)) [f(x)]_(x=0) .(n in z).

if f(X) =|{:(x^(n),,n!,,2),(cos x,,cos.(npi)/(2),,4),(sin x,,sin .(npi)/(2),,8):}|, then find the value of (d^(n))/(dx^(n)) [f(x)]_(x=0) .(n in z).

if f(x)=|{:(x^(n),,n!,,2),(cos x,,cos.(npi)/(2),,4),(sin x,,sin .(npi)/(2),,8):}|, then find the value of (d^(n))/(dx^(n)) [f(x)]_(x=0) .(n in z).

if =|{:(x^(n),,n!,,2),(cos x,,"cos"(npi)/(2),,4),(sin x,,"sin" (npi)/(2),,8):}|, then find the value of (d^(n))/(dx^(n)) [f(x)]_(x=0) (n in z)

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

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

If f(x)=det[[x^(n),n!,2cos x,cos((n pi)/(2)),4sin x,sin((n pi)/(2)),8]], then find the value of (d^(n))/(dx^(n))[f(x)]_(x=0)]|

If f(x)=|(x^n, sinx, cosx),(n!, sin((npi)/2), cos((npi)/2)),(a, a^2,a^3)| , then show that d^n/dx^n [f(x)] at x=0 is 0