Continuity and ...

If $$f(x)={ sin }^{ -1 }\left[ \dfrac { 2x }{ 1+{ x }^{ 2 } }  \right] $$,then $$f(x)$$ is differentiable on 

f(X)=|x|+|x-1| is continuous at 

If $$f\left( x \right) = {\left| x \right|^{\left| {\sin x} \right|}}$$, then $${f'}\left( { - \dfrac{\pi }{4}} \right)$$ is equals

f(x) is diffrentiable function and (f(x). g(x)) is differentiable a x=a , then 

The order of the differential equation of all circles whose radius is $$4$$, is?

Give that f(x) =xg(x) /$$ \left | x \right | $$ , g(0) = 0 and f(x) is continous at x=0. Then the value of f' (0)

If $$f(x) =  \left\{\begin{matrix} \dfrac{x\log \cos x}{\log(1+x^2)}, & x \neq 0\\ 0, & x=0\end{matrix}\right.$$ then

Let $$f:(-1,1)\rightarrow R$$ be a differentiable function satisfying 
             $$(f'(x))^4=16(f(x))^2$$ for all $$x\in (-1,1)$$
   $$f(0)=0$$
The number of such functions is 

Let $$f(x)$$ be a function satisfying $$f(x+y)  = f(x)+f(y)$$ and $$f(x) = xg(x)$$ $$\forall x, ~y \in$$ R, where $$g(x)$$ is a continuous function then, which of the following is true?

If the function $$f:[0,8] \rightarrow R$$ is differentiable, then for$$0<a, b<2, \int_{0}^{8} f(t) d t$$ is equal to