ðɪs tˈɛlz ˌʌs ðætðə tˈoʊɾəl ɹˈeɪt ʌv tʃˈeɪndʒ ʌvðə fˈʌŋkʃən ˈɛf æz ðə flˈuːɪd pˈɑːɹsəlz mˈuːvz θɹuː ɐ flˈoʊ fˈiːld dᵻskɹˈaɪbd baɪ ɪts juːlˈɪɹiən spˌɛsɪfɪkˈeɪʃən jˈuː ɪz ˈiːkwəl tə ðə sˈʌm ʌvðə lˈoʊkəl ɹˈeɪt ʌv tʃˈeɪndʒ ænd ðə kənvˈɛktɪv ɹˈeɪt ʌv tʃˈeɪndʒ ʌv ˈɛf. ðɪs ɪz ɐ kˈɑːnsɪkwəns ʌvðə tʃˈeɪn ɹˈuːl sˈɪns wiː ɑːɹ dˌɪfɚɹˈɛnʃɪˌeɪɾɪŋ ðə fˈʌŋkʃən ˈɛf ˈɛks ˈɛks zˈiəɹoʊ, tˈiː, tˈiː wɪð ɹᵻspˈɛkt tə tˈiː.
This tells us that the total rate of change of the function F as the fluid parcels moves through a flow field described by its Eulerian specification u is equal to the sum of the local rate of change and the convective rate of change of F. This is a consequence of the chain rule since we are differentiating the function F(X(x0, t), t) with respect to t.