Uniformly continuous with unbounded derivative

Taking $$f(x)=\frac{\cos(x^3)}{x}$$ on $[1,\infty)$ suffices since it is uniformly continuous and has the following derivative:

$$f’(x)=-3x\sin(x^3)-\frac{\cos(x^3)}{x^2}.$$

Tags:

Real Analysis

Uniform Continuity

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