Continuity and ...

The function given by y=$$ \left | x-1 \right | $$ is differentiable function and $$ f(1/n) $$ = 0 $$ \forall n\geq 1 $$ and n\epsilon I $$, then

 The largest value of c such that there exists a differential function $$ h(x) for  -c < x < c $$ that is a solution of $$ y_1 = 1 +y^2 $$ with h(0) = 0 is 

If $$y=\sin^{-1}\left\{\dfrac{\sqrt{1+x}+\sqrt{1-x}}{2}\right\}$$ then $$\dfrac{dy}{dx}=$$

If $$y=\tan^{-1}\left\{\dfrac{\sqrt{1+x^{2}}-1}{x}\right\}$$ then $$\dfrac{dy}{dx}=?$$

If $$y=\sec^{-1}\left(\dfrac{1}{2x^{2}-1}\right)$$ then $$\dfrac{dy}{dx}=?$$

Which of the following function is thrice differentiable at x=0?

If $$y=\sec^{-1}\left(\dfrac{x^{2}+1}{x^{2}-1}\right)$$ then $$\dfrac{dy}{dx}=?$$

 If $$y=\tan ^{-1} \sqrt{\dfrac{x+1}{x-1}}, $$ then $$ \dfrac{d y}{d x} $$ is

If $$P(1)=0$$ and $$\dfrac {dP(x)}{dx} > P(x)$$ for all $$x \ge 1$$, then

The function $$ f(x)=\dfrac{x}{1+\left | x \right |} $$ is differentiable