f(x)=(1+x)(1+x^(2))(1+x^(4))(1+x^(8))," prove that "f'(1)=120

If f(x) = (1 + x) (1 + x^(2)) (1 + x^(4)) (1 + x^(8)) , then f'(1) is

Find the derivative of the function f(x) given by f(x)=(1+x)(1+x^(2))(1+x^(4))(1+x^(8)) and hence find f'(1)

If f(x)=(x^(2))/(1+x^(2)), prove that lim_(x rarr oo)f(x)=1

If f(x)=(x^(2)-1)/(x^(2)+1) prove that f((1)/(x))=-f(x)

(i) If f(x) = x + (1)/(x) prove that: [f(x)]^(3) = f(x^(3)) + 3f ((1)/(x)) (ii) If f(x) = x^(3) - (1)/(x^(3)) , prove that f(x) + f((1)/(x)) = 0 (iii) If f(x) = (1-x^(2))/(1+ x^(2)) , prove that f (tan theta) = cos 2 theta

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

If f(x) = log_e ((1+x)/(1-x)) , prove that f((2x)/(1+x^2))=2f(x) .

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

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

If f(x)=(1-x)/(1+x) , then prove that f(x)+f(1/x)=0 .