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

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).

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))

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

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

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

Simplify : ((a^(m))/(a^(n)))^(m+n)((a^(n))/(a^(l)))^(n+l)((a^(l))/(a^(m)))^(l+m)

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

Show that : ((a^(m))/(a^(-n)))^(m-n)xx((a^(n))/(a^(-1)))^(n-1)xx((a^(l))/(a^(-m)))^(l-m)=1

The point of intersection of tangents drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at the points where it is intersected by the line l x+m y+n=0 , is ((-a^2l)/n ,(b^2m)/n) (b) ((-a^2l)/m ,(b^2n)/m) ((a^2l)/m ,(-b^2n)/m) (d) ((a^2l)/m ,(b^2n)/m)