$${e^z}$$ is a periodic with a period of

For the differential equation $$f\left( {x,y} \right){{dy} \over {dx}} + g\left( {x,y} \right) = 0\,\,$$ to be exact is

If $$\varphi \left( x \right) = \int\limits_0^{{x^2}} {\sqrt t \,dt\,} $$ then $${{d\varphi } \over {dx}} = \_\_\_\_\_\_\_.$$

If $$y = \left| x \right|$$ for $$x < 0$$ and $$y=x$$ for $$x \ge 0$$ then