I'm watching a online tutorial Transport equation, derivation at 9:35 it states the following
Let $u$ be a function of $x,t$ $$\frac{d}{dt}u(ct+x_0,t) = \frac{\partial u(ct+x_0,t)}{\partial x}\frac{d(ct+x_0)}{dt}+\frac{\partial u(ct+x_0,t)}{\partial t}\frac{d(t)}{dt}$$ I don't understand why the derivative of $u$ with respect to $t$ contains a $\frac{\partial u}{\partial x}$ term when derivation is only with respect to $t$.
Could anyone explain this derivation ?