The linear approximation of a function z = f ( x , y ) {\displaystyle \displaystyle z=f(x,y)} at a point ( p x , p y ) {\displaystyle \displaystyle (p_{x},p_{y})} is
z = f ( x , y ) ≈ f ( p x , p y ) + ( x − p x ) ∂ z ∂ x ( p x , p y ) + ( y − p y ) ∂ z ∂ y ( p x , p y ) {\displaystyle \displaystyle z=f(x,y)\approx f(p_{x},p_{y})+(x-p_{x}){\frac {\partial z}{\partial x}}(p_{x},p_{y})+(y-p_{y}){\frac {\partial z}{\partial y}}(p_{x},p_{y})}
at a point 
is
