If t = x + 4 , then ((dx)/(dt)) _ t = 4 is:

Given that $t = \sqrt{x} + 4$

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

Differentiating the above equation with respect to time,

$⇒ \dfrac{dx}{dt} = 2t - 8$

Putting the value of $t = 4$

$⇒ \dfrac{dx}{dt} = 2 \times 4 - 8 = 0$