If `y=tan^(-1)((2^x)/(1+2^(2x+1))),t h e n(dy)/(dx)a tx=0` is (a)1 (b) 2 (c) 1n 2 (d) none of these

if y=tan^(-1)((2^(x))/(1+2^(2x+1))) then (dy)/(dx)atx=0 is

f'(x)=sqrt(2x^(2)-1) and y=f(x^(2)), then (dy)/(dx) at x=1 is 2(b)1(c)-2 (d) none of these

If y = tan ^(-1) ((2x)/(1-x^(2))) , " then " (dy)/(dx) =____________

f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim_(x->oo)f(x) is equal to (a) 1 (b) 1/2 (c) 2 (d) none of these

If x=e^(-t^(2)), y=tan^(-1)(2t+1) , then (dy)/(dx)=

e^(x)=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t)) andtan (y)/(2)=sqrt((1-t)/(1+t)) then (dy)/(dx) at t=(1)/(2) is (a)-(1)/(2) (b) (1)/(2)(c)0(d) none of these

If x^(2)+y^(2)=t-(1)/(t) and x^(4)+y^(4)=t^(2)+(1)/(t^(2)) then x^(3)y(dy)/(dx)=(a)0(b)1(c)-1(d) non of these

If tan y=(2^(x))/(1+2^(2x+1)), then (dy)/(dx) at x=0 is -(3)/(10) (b) -(3)/(10)ln2-(1)/(10)(d)-(1)/(10)ln2