i need to prove that $\displaystyle f(x)=ln(x^{2}+cos^{2}x) $ is uniformly continous. now, i thought of a way. i know that $\displaystyle f'(x)=\frac{2x-sin2x}{x^{2}+cos^{2}x} $

so i acctually need to prove that $\displaystyle f'(x) $ is bounded ($\displaystyle N\leq f'(x)\leq M $). but how do i prove it?