The contravariant partial derivative is defined as following: $$\partial ^\mu = \frac{\partial}{\partial x_\mu}$$ where the index $\mu$ runs from 0 to 3. A contravariant vector under Lorentz transformation (at leas in Physics textbooks) is defined as: $$q'^\mu = \Lambda ^\mu _\rho q^\rho $$
Now what I don't get is why is the partial derivative above a contravariant 4-vector (the contravariant part, not the factor that it is a 4-vector).