I am listening to a differential geometry lecture this semester, after the Definition of the Christoffel symbols of a connection $\nabla$ it says that
[...] the first term is strongly dependent on the chart.
in regards to the formula
$$\nabla_XY = \sum_k \bigg( \sum_i X_i \dfrac{\partial Y_k}{\partial x_i} + \sum_{ij} X_i Y_j\Gamma_{ij}^k \bigg) \dfrac{\partial }{\partial x_k}$$
for a chart $(U, \varphi = (x_1, \ldots, x_n))$ of a smooth Manifold $M$ and two vectorfields $$X = \sum_i X_i \dfrac{\partial }{\partial x_i}\quad \text{and}\quad Y = \sum_j Y_j \dfrac{\partial}{\partial x_j}.$$
How can I see that there is a "strong dependence" or rather, what does it mean to be strongly dependent on a chart?