You will have to use the chain rule when differentiating the square roots, because you are differentiating a composite function (function within a function)
When differentiating sqrt[x^2+144] let h(x) = sqrt[x], let g(x) = [x^2+144]
d/dx sqrt[x^2 + 144] = h'(g(x))g'(x)
Do the same for the second square root, and then add the derivatives (sum rule)