Find the Derivative of the Function $$g ( x ) = \int _ { 4 } ^ { x ^ { 2 } } 4 \sqrt { 1 + t ^ { 2 } } d t$$

Find the derivative of the function.
$$g ( x ) = \int _ { 4 } ^ { x ^ { 2 } } 4 \sqrt { 1 + t ^ { 2 } } d t$$