Application Of Derivatives

Let \(f(x)\) be differentiable on the interval (0, \(\infty\)) such that \(f(1)=1\), and \(\mathop {\lim }\limits_{t \to x} {{{t^2}f(x) - {x^2}f(t)} \over {t - x}} = 1\) for each \(x > 0\). Then \(f(x)\) is