if `f(x) = (x^l/x^m)^(l+m) (x^m/x^n)^(m+n) (x^n/x^l)^(n+l)` then find f'(x).

If f(x)=((x^l)/(x^m))^(l+m)((x^m)/(x^n))^(m+n)((x^n)/(x^l))^(n+l) , then f'(x)

If f(x)=((x^l)/(x^m))^(l+m)((x^m)/(x^n))^(m+n)((x^n)/(x^l))^(n+l) , then f^(prime)(x) is equal to (a) 1 (b) 0 (c) x^(l+m+n) (d) none of these

Simplify: (i)\ ((x^(a+b))/(x^c))^(a-b)\ ((x^(b+c))/(x^a))^(b-c)\ ((x^(c+a))/(x^b))^(c-a) (ii)\ ((x^l)/(x^m))^(1/(lm))\ xx\ ((x^m)/(x^n))^(1/(mn))\ xx\ \ ((x^n)/(x^l))^(1/(ln))

if f (x) = lim _(x to oo) (prod_(i=l)^(n ) cos ((x )/(2 ^(l)))) then f '(x) is equal to:

(x^(m+n)xxx^(n+l)xxx^(l+m))/(x^mxxx^nxxx^l)

Let m and n be positive integers and x,y gt 0 and x+y =k, where k is constant. Let f (x,y) = x ^(m)y ^(n), then: (a) f (x,y) is maximum when x= (mk)/(m+n) (b) f (x,y) is maximuim where x =y (c) maximum value of f (x,y) is (m^(n)n ^(m) k ^(m+n))/((m+n)^(m+n)) (d) maximum value of f (x,y) is (k ^(m+n) m ^(m)n ^(n))/((m+n)^(m+n))

if f(x)=(x^(3)-3x^(2)+3x-x^(2)l n(e^((1)/(x^(2)))(x^(2)-x+2)))/(l n(x^(2)-x+2)) then f^('')(1) is equal to

If f(x)=lim_(m->oo) lim_(n->oo)cos^(2m) n!pix then the range of f(x) is

Statement.1 : The function f (x) =lim _(xtooo) (log _(e)(1+x) -x ^(2n) sin (2x))/(1+ x ^(2n)) is discontinuous at x=1 Statement.2: L.H.L. =R.H.L.ne f (1).

Differential coefficient of (x^((l+m)/(m-n)))^(1//(n-l))*(x^((m+n)/(n-l)))^(1//(l-m))*(x^((n+l)/(l-m)))^(1//(m-n)) wrt x is