If `f(x)=(1+1/x)(1+2/x)(1+3/x)........(1+n/x). x!=0`.Then`f'(-1)=`

If f(x)=(1+x)(2+x^(2))^((1)/(2))(3+|x^(3)|)^((1)/(3)) then f'(-1) is

Let f(x)=x+(1-x)x^3+(1-x)(1-x^2)x^3+.........+(1-x)(1-x^2)........(1-x^(n-1))x^n;(n >= 4) then :

If f(x)=(1-x)/(1+x)" then "f(x)+ f(1/x)=...... where (x)in R-{0,1}.

If f(x)=(1+x)(1+x^2)(1+x^3)(1+x^4) , then f'(0)=1

Let f(x)=x+(1-x)x^(3)+(1-x)(1-x^(2))x^(3)+.........+(1-x)(1-x^(2))......*(1-x^(n-1))x^(n);(n>=4) then :

Let f(x)=x+(1-x)x^(2)+(1-x)(1-x^(2))x^(3)+............+(1-x)(1-x^(2)).........(1-x^(n-1))x^(n);(n) then :

If f(x)=(1-x)/(1+x), prove that f{f((1)/(x))}=1/x[x ne0]

f(x)={(x)/(1+x)+(x)/((1+x)(1+2x))+(x)/((1+2x)(1+3x))+....n terms} and x gt 0 then Lt_(x to oo)f(x)=

If f(x) =|(1, x, x+1),(2x, x(x-1), x(x+1)), (3x(x-1), 2(x-1)(x-2), x(x+1)(x-1))| then what is f(-1) +f(0) +f(1) equal to ?

If f(x)={:{((e^(1/x)-1)/(e^(1/x)+1)", for " x !=0),(1", for " x=0):} , then f is