Let \( f(x) \) be a continuously differentiable function on the interval \( (0, \infty) \) such that\( f(1) = 2 \) and
\( \displaystyle \lim_{t \to x} \frac{t^{10} f(x) - x^{10} f(t)}{t^{9} - x^{9}} = 1 \)
for each \( x > 0 \). Then, for all \( x > 0 \), \( f(x) \) is equal to:
