If `a=x^(m+n)\ y^l,\ b=x^(n+l)\ y^m` and `c=x^(l+m)y^n ,` prove that `a^(m-n)\ b^(n-l)\ c^(l-m\ )=1`

If a = x^(m + n) . Y^(l), b = x^(n + l). Y^(m) and c = x^(l + m) . Y^(n) , Prove that : a^(m-n) . b^(n - 1) . c^(l-m) = 1

If x=a^(m+n),\ y=a^(n+l) and z=a^(l+m) , prove that x^m y^n z^l=x^n y^l z^m

If y=(x-a)^(m)(x-b)^(n) , prove that (dy)/(dx)=(x-a)^(m-1)(x-b)^(n-1)[(m+n)x-(an+bm) ].

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

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

If the line l x+m y+n=0 touches the parabola y^2=4a x , prove that ln=a m^2

If the line l x+m y+n=0 touches the parabola y^2=4a x , prove that ln=a m^2

If L(m,n)=int_(0)^(1)t^(m)(1+t)^(n),dt , then prove that L(m,n)=(2^(n))/(m+1)-n/(m+1)L(m+1,n-1)

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^(prime)(x) is equal to (a) 1 (b) 0 (c) x^(l+m+n) (d) none of these