The first partial derivative $f_x(a,b)$ of $f(x,y)$ is the derivative of $f(x,y)$ at $(a,b)$ in the direction of the positive $x$ axis. Similarly, the first partial derivative$f_y(a,b)$ in the derivative of $f(x,y)$ at $(a,b)$ toward the positive $y$ axis. We can also consider any direction in the tangent plane at $\bigl(a,b,f(a,b)\bigr)$ on the surface graph of $f$. If we take a tangent vector of length $1$, then we get the following definition.