Let

$f(x)=e^{\sqrt[\phantom{2}]{x^2+4}}$

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

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

$f^{\text{'}}(x)=\frac{x*e\sqrt[\phantom{2}]{x^2+4}}{\sqrt[\phantom{2}]{x^2+4}}.$

$f^{\text{'}}(x)=e^{\sqrt[\phantom{2}]{x^2+4}}.$

The domain of $f$ is $R.$

$f^{\text{'}}(0)=e^4.$

$f^{\text{'}}(x)=2*x*e^{\sqrt[\phantom{2}]{x^2+4}}.$

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

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