Since the partial derivative ( ∂ ∂ u ∂ ∂ T ) V can be expressed as a relationship between only u and T (if one isolates it on one side of the equality), the partial derivative can be replaced by the ordinary derivative. After separating the differentials the equality becomes d u 4 u = d T T , which leads immediately to u = A T 4 , with A as some constant of integration.