`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)=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 the value of (d^(n))/(dx^(n))(f(x))" at "x=0" for "n=2m+1 is

If A(x)=det[[x^(n),sin x,cos xn!sin((n pi)/(2)),cos((n pi)/(2))a,a^(2),a^(3)]], then the value of (d^(n))/(dx^(n))[Delta(x)] at x=0 is

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

Let I_(n)int_(0)^((pi)/(2))(sin x+cos x)^(n)dx(n>=2) Then the value of nI_(n)-2(n-1)I_(n-2) is

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 "

If s in x+cos ecx=2, then write the value of sin^(n)x+cos ec^(n)x

If x!=(n pi)/(2),n in I and (cos x)^(sin)(2x-3sin x+2)=1, then find the general solution of x.