The Variable That Sits Still

A thin rectangular metal plate is heated from one edge. With $x$ and $y$ measured in centimetres from the centre of the plate (so both can be negative), the temperature at the point $(x,\,y)$ is

$T(x,\,y) = x^2 y^3 - 4xy + 9y^2 + 40$

measured in degrees Celsius.

A probe rests at the point $(-2,\,3)$. It is nudged a tiny distance in the $x$-direction only — the $y$-coordinate stays locked at $3$ the entire time.

What is $\dfrac{\partial T}{\partial x}$ at the point $(-2,\,3)$?

The answer is a whole number. Include the sign.