If t = x + 4 , then d x d t t = 4 is:

Given that $t=\sqrt{x}+4$

$\Rightarrow x={\left(t-4\right)}^2=t^2-8t+16$

Differentiating the above equation with respect to time,

$\Rightarrow \frac{\mathrm{d}x}{\mathrm{d}t}=2t-8$

Putting the value of $t=4$

$\Rightarrow \frac{dx}{dt}=2\times 4-8=0$