if y=1/2ln(x^2+5), then dy/dx=

Is ln(x^2+5) in the denominator? If so, use brackets to distinguish

1/[2ln(x^2+5)] from
(1/2)ln(x^2+5)

In either case, I suggest treating x^2+5 as a new variable, u, and using the chain rule.
df/dx = (df/du)(du/dx)