If `y=(x/n)^(n x)(1+logx/n)`, then `y'(n)` is given by

If y=((x)/(n))^(nx)(1+(log x)/(n)), then y'(n) is given by

If y=x^(n)logx+x(logx)^(n)," then "(dy)/(dx) is equal to

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

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

If I_(m,n) - int (x^(m) (logx)^(n) dx then I_(m,n) - (x^(m+1))/((m + 1)) (logx)^(n) =

If y=x^((logx)^("log"(logdotx))),t h e n(dy)/(dx)i s (a) y/x(1n x^(x-1))+21 nx1n(1nx)) (b) y/x(logx)^("log"(logx))(2log(logx)+1) (c) y/(x1nx)[(1nx)^2+21 n(1nx)] (d) y/x(logy)/(logx)[2log(logx)+1]

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

If y=x^((logx)^("log"(logdotx))),t h e n(dy)/(dx)i s (a)y/x(1n x^(oox-1))+21 nx1n(1nx)) (b)y/x(logx)^("log"(logx))(2log(logx)+1) (c)y/(x1nx)[(1nx)^2+21 n(1nx)] (d)y/x(logy)/(logx)[2log(logx)+1]

If y=x^((logx)^("log"(logdotx))),t h e n(dy)/(dx)i s (a) y/x(1n x^(oox-1))+21 nx1n(1nx)) (b) y/x(logx)^("log"(logx))(2log(logx)+1) (c) y/(x1nx)[(1nx)^2+21 n(1nx)] (d) y/x(logy)/(logx)[2log(logx)+1]

If x_(n) + iy_(n) = (1 + i)^(n) then x_(n - 1) y_(n) - x_(n) y_(n- 1) =