Continuity and ...

If $$f(x)=a|\sin x|+ be^{|x|}+c|x|^{3}$$, where $$a,b,c\in R$$, is differentiable at $$x=0$$, then 

If $$y=\tan{x}$$, then $$\dfrac{d^{2}y}{dx^{2}}=$$

Let $$g$$ is the inverse function of $$f$$ and $$f'(x)=\dfrac {x^{10}}{(1+x^{2})}$$. If $$g(2)=a$$ then $$g'(2)$$ is equal to

If $$f\left( x \right) =\left\{ \dfrac { x }{ { e }^{ { 1 }/{ x } }+1 }  \right\} $$ when $$x\neq 0,$$ then 0,when x=0

If $$y=\sin^{-1}\dfrac{2x}{1+x^{2}}$$ then $${ \dfrac {dy}{dx} }$$ is :

If for $$x \in \left(0, \dfrac{1}{4}\right)$$, the derivative $$\tan^{-1} \left(\dfrac{6x\sqrt{x}}{1-9x^{3}}\right)$$ is $$\sqrt{x}.g(x)$$, then $$g(x)$$ equals :

If $$y = \exp \left\{ {{{\sin }^2}x + {{\sin }^4}x + {{\sin }^6}x + ....} \right\}$$ then $$\frac {dy}{dx}=$$

The function $$f\left( x \right) = \dfrac{{4 - {x^2}}}{{4x - {x^3}}}$$ is

If $$\dfrac {dy}{dx}=(e^ {y}-x)^ {-1}$$ where $$y(0)=0$$ then $$y$$ is expressed explicity as 

If $$x\dfrac{dy}{dx}=y(\log y-\log x +1)$$, then the solution of the equation