Solution
= Solution
In a <holomorphic coordinate> chart, $T^{1,0}X$ has frame $\partial/\partial z^1,\ldots,\partial/\partial z^n$. Under a holomorphic coordinate change $w=w(z)$, the <chain rule> gives
$$
\frac{\partial}{\partial z^j}=\sum_k\frac{\partial w^k}{\partial z^j}\frac{\partial}{\partial w^k}.
$$
The Jacobian is an invertible matrix of <holomorphic functions>. These frames therefore make $T^{1,0}X$ the <holomorphic tangent bundle>.