[" Let "(d)/(dx)(f(x))=((sin^(12)x-cos^(12)x))/((sin^(2)x-cos^(2)x)(1-3sin^(2)x cos^(2)x))" be such that "f(0)=0],[(k pi)/(16)." Find the value of "k(k in N)]

Let (d)/(dx)(f(x))=((sin^(12)x-cos^(12)x)/((sin^(2)x-cos^(2)x)(1-3sin^(2)x cos^(2)x))) be such that f(0)=0 then f((pi)/(2)) equals (k pi)/(16). Find the value of k(k in N)

If (d)/(dx)[int_(0)^(g(x))f(t)dt]=2x sin(2x^(2))e^(a sin^(2)(x^(2)))cos(b sin x^(2)) then

"Let "f(x)=|{:(cos(x+x^(2)),sin (x+x^(2)),-cos(x+x^(2))),(sin (x-x^(2)),cos (x-x^(2)),sin (x-x^(2))),(sin 2x, 0, sin (2x^(2))):}|. Find the value of f'(0).

"Let "f(x)=|{:(cos(x+x^(2)),sin (x+x^(2)),-cos(x+x^(2))),(sin (x-x^(2)),cos (x-x^(2)),sin (x-x^(2))),(sin 2x, 0, sin (2x^(2))):}|. Find the value of f'(0).

"Let "f(x)=|{:(cos(x+x^(2)),sin (x+x^(2)),-cos(x+x^(2))),(sin (x-x^(2)),cos (x-x^(2)),sin (x-x^(2))),(sin 2x, 0, sin (2x^(2))):}|. Find the value of f'(0).

"Let "f(x)=|{:(cos(x+x^(2)),sin (x+x^(2)),-cos(x+x^(2))),(sin (x-x^(2)),cos (x-x^(2)),sin (x-x^(2))),(sin 2x, 0, sin (2x^(2))):}|. Find the value of f'(0).

If d/(dx) (f(x))^(n)=n(f(x))^(n-1)(df(x))/(dx) then (d)/(dx) (sin^3x)=3sin^(2)x.cosx .

If k_(1)=sin x cos^(3)x and k_(2)=cos x sin^(3)x then

Let (d)/(dx)(F(x))=(e^(sin x))/(x),x>0. If int_(1)^(4)2(e^(sin(x^(2))))/(x)dx=F(k)-F(1), then possible value of k is: