Hi guys! I am recently reading Nonlinear Solid Mechanics A Continuum Approach for Engineering by Gerhard A. Holzapfel, Chapter 2.3 and was confused with one equation. You can refer to this stackexchange link for more detail (https://physics.stackexchange.com/questions/558789/why-the-material-time-derivative-of-a-material-field-f-equals-to-the-direction). In short, this equation states that the the material time derivative of a material field 𝐹 equals to the directional derivative of 𝐹 in the direction of the velocity vector 𝑣. I tried to prove this equation but failed and the process has been attached in the stackexchange post. Can someone help me with this?

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