Answer
$\dfrac{\sec x(1+x\tan x)}{2\sqrt{7+x\sec x}}$
Work Step by Step
Consider the derivative of function $f(x)$ as follows:
$f'(x)=(\dfrac{1}{2})(7+x\sec x)^{-(1/2)}(7+x\sec x)'=(\dfrac{1}{2})(7+x\sec x)^{-(1/2)}((0)+(x)'\sec x+x(\sec x)'\Big)=\dfrac{\sec x(1+x\tan x)}{2\sqrt{(7+x\sec x)}}$
