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 =|{:(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, 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

If f(x)=|{:(x^(n),sinx,cosx),(n!,"sin"(npi)/(2),"cos"(npi)/(2)),(a,a^(2),a^(3)):}| , then the value of (d^(n))/(dx^(n))(f(x))" at "x=0" for "n=2m+1 is

If f(x)=(a^(x))/(a^(x)+sqrt(a)),(a>0), then find the value of sum_(r=1)^(2n1)2f((r)/(2n))

f(x)=e^(x)-e^(-x)-2sin x-(2)/(3)x^(3). Then the least value of n for which (d^(n))/(dx^(n))f(x)|_(x=0) is nonzero is 5(b)6(c)7(d)8

If f(x) = x+3x^2+5x^4+7x^8+... to n terms then find the value of f'(1) .

Let "f(x)"|{:(pi^n,sinpix,cospix),((-1)^(n)!,-sin((npi)/2),-cos((npi)/2)),(-1,1/sqrt2,sqrt3/2):}| Then value or d^n/(dx^n)["f(x)"]"at "x=1" is "