According to the chain rule, d/dx [f(g(x))] = f'(g(x)) * g'(x). Here, let f(u) = cos(u) where u = x² + 5. The derivative of the outer function f(u) is -sin(u), and the derivative of the inner function u = x² + 5 is 2x. Multiplying them together, we get dy/dx = -sin(x² + 5) * (2x) = -2x * sin(x² + 5). Option A misses the negative sign required for the derivative of cosine. Option C forgets to differentiate the inner function (the 2x term). Option D incorrectly keeps the cosine function instead of changing it to sine.