" 20."y=x^(n)+n^(x)+x^(x)+n^(n)

Find (dy)/(dx) if,y=x^(n)+n^(x)+x^(x)+n^(n)

If x ^(n) y^(n) =( x+y ) ^(n),then (dy)/(dx)=

If x^(n) y^(n) =(x+y) ^(n),then (dy)/(dx)=

If the arithmetic mean of x and y be (x^(n+1)+ y^(n+1))/(x^(n) + y^(n)) , then find n.

x^n - y^n = (x-y) (x^(n-1) + x^(n-2) y + … + xy^(n-2) + y^(n-1)) , x,y in R

The value of n for which (x^(n+1)+y^(n+1))/(x^(n)+y^(n)) is the geometric mean of x nd y is

If x + y = 1, show that D ^ (n) (x ^ (n) y ^ (n)) = n! [Y ^ (n) - (nC_ (1)) ^ (2) y ^ (n -1) x + (nC_ (2)) ^ (2) y ^ (n-2) x ^ (2) + ...... + (- 1) ^ (n) x ^ (n)]

If A=([x,x],[x,x]) then A^(n)(n in N)= 1) ([2^nx^n,2^nx^n],[2^nx^n,2^nx^n]) 2) ([2^(n-1) x^n,2^(n-1) x^n],[2^(n-1) x^n,2^(n-1) x^n]) 3) I 4) ([2^(n) x^(n-1),2^(n) x^(n-1)],[2^(n) x^(n-1),2^(n) x^(n-1)])

If |[x^(n-1), x^(n+1), x^(n+2)] ,[y^(n-1), y^(n+1), y^(n+2)], [z^(n-1), z^(n+1), z^(n+2)]|= (x-y)(y-z)(z-x)(x^(-1)+y^(-1)+z^(-1)) then n=