Differentiating Vectors Using Chain Rule: Textbook Clarification

Question

My textbook has the following:

My question is, isn't the chain rule $\dfrac{ \partial{f} }{ \partial{g} } \dfrac{ dg }{ dt } + \dfrac{ \partial{f} }{ \partial{h} } \dfrac{ dh }{dt }$?

Answer 1

Maybe it becomes clearer if you set:

• $x=x(t)$ and $y=y(t)$

instead of

• $x=g(t)$ and $y=h(t)$.

So it is just using different symbols.