In Arfken and Webber's "Mathematical Methods for Physicists" under the topic "General Tensors" the following is given: $$dx^i=\frac{\partial x^i}{\partial q^j}dq^j$$ or in vector form, $$d\textbf r=\vec\epsilon_jdq^j$$ such that $$\vec\epsilon_j=\frac{\partial\textbf r}{\partial q^j} \ \ \ \ \ \ \ \ \ \ \ \ (1) $$
Till here things are fine,
he then writes $$\vec\epsilon_1=\bigg(\frac{\partial x^1}{\partial q^1},\frac{\partial x^1}{\partial q^2},\frac{\partial x^1}{\partial q^3}\bigg) $$
But shouldn't it be$$\vec\epsilon_1=\bigg(\frac{\partial x^1}{\partial q^1},\frac{\partial x^2}{\partial q^1},\frac{\partial x^3}{\partial q^1}\bigg) $$ from $(1)$?
EDIT: I am adding the screenshot (though I have included the relevant details in the question) just for the sake of completeness and clarity.
