Science:Math Exam Resources/Courses/MATH105/April 2011/Question 08 (b)/Hint 1

If $g(x,y)$ is a differentiable function of two variables x and y, then near any specific point (x₀, y₀) we have the linear approximation

$\displaystyle g(x,y)\approx g(x_{0},y_{0})+\left({\frac {\partial g}{\partial x}}(x_{0},y_{0})\right)\cdot (x-x_{0})+\left({\frac {\partial g}{\partial y}}(x_{0},y_{0})\right)\cdot (y-y_{0})$