If `f (x) =|(1,1,1),(1,x,x^2),(1,x^2,x^3)|,` then `f prime (x)` vanishes at :

If f(x)=det[[1,1,11,x,x^(2)1,x^(2),x^(3)]], then f'(x) vanishes

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

If f(x-1)=f(x+1) , where f(x)=x^2-2x+3 , then: x=

If f(x)=1-x+x^2-x^3+......-x^(99)+x^(100) then f^(prime)(1) equals

If f(x)=1+x+(x^2)/2++(x^(100))/(100), then f^(prime)(1) is equal to

Let f(x)=|(1,x,x^(2)),(x,x^(2),1),(x^(2),1,x)| then |f(2.9)^(1//3)|= ___________

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

If f_r(x),g_r(x),h_r(x),r=1,2,3 are polynomials such that f_r(a)=g_r(a)=h_r(a),r=1,2,3 and F(x)=|[f_1(x),f_2(x),f_3(x)],[g_1(x),g_2(x),g_3(x)],[h_1(x),h_2(x),h_3(x)]| then F^(prime)(x) at x=a is____________________

If f_r(x),g_r(x),h_r(x),r=1,2,3 are polynomials such that f_r(a)=g_r(a)=h_r(a),r=1,2,3 and F(x)=|[f_1(x),f_2(x),f_3(x)],[g_1(x),g_2(x),g_3(x)],[h_1(x),h_2(x),h_3(x)]| then F^(prime)(x) at x=a is____________________

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