If `y=(1-x)^(-alpha)e^(-alphax),x!=1` then

If y=1/(1+x^(beta-alpha)+x^(gamma-alpha))+1/(1+x^(alpha-beta)+x^(gamma-beta))+1/(1+x^(alpha-gamma)+x^(beta-gamma)), then (dy)/(dx) is equal to-

Let A=[(x,2y),(-1,y)], x , y in R If AA'= [(1,0),(0,alpha)] (alpha in R) , then alpha+y^2 is equal to :

(lim_(x rarr){((n)/(n+1))^(alpha)+s in(1)/(n)]^(n) (when alpha in Q ) is equal to (a) e^(-alpha)(b)-alpha(c)e^(1-alpha)(d)e^(1+alpha)

Let f(x)=(alphax)/(x+1),x ne -1 . Then, for what values of alpha is f[f(x)]=x?

Suppose that F(alpha) denotes the area of the region bounded by x = 0, x=2, y^2=4x and y=|alphax-1|+|alphax-2|+alphax, where alpha in {0,1}. Then the value of F(alpha)+(8sqrt(2))/3 when alpha = 0 is (A) 4 (B) 5 (C) 6 (D) 9

If y=1+(alpha)/(((a)/(x)-alpha))+(beta/x)/(((1)/(x)-1)((1)/(x)-beta))+(gamma/x^(2))/(((1)/(x)-alpha)((1)/(x)-beta)((1)/(x)-gamma)) find (dy)/(dx)

If y=tan^(-1)((2)/(e^(-x)-e^(x)))" then "(1+e^(2x))y_(1)=

If y=log(e^(-x)+xe^(-x))," then " (1+x)y_(1)=