Let

$f(x)=e^{\sqrt[\phantom{2}]{5*x^2+2}}$

Tick all of the following statements that are correct. Marks will be removed for incorrect answers.

The domain of $f$ is $[0,).$

$f^{\text{'}}(x)=\frac{5*x*e^{\sqrt[\phantom{2}]{5*x^2+2}}}{\sqrt[\phantom{2}]{5*x^2+2}}$

$f^{\text{'}}(x)=e^{\sqrt[\phantom{2}]{5*x^2+2}}$

The domain of $f$ is $R.$

$f^{\text{'}}(0)=e^2.$

$f^{\text{'}}(x)=10*x*e^{\sqrt[\phantom{2}]{5*x^2+2}}$

$f^{\text{'}}(1)>0.$

$f^{\text{'}}(x)>0$ for all $x>0.$