Chapter 4.5, Problem 258E

The x and y components of a fluid moving in two dimensions are given by the following functions:

u(x. y) = 2y and $v\left(x,y\right)=-2x;x\ge 0;y\ge 0$ . The

speed of the fluid at the point (x. y) is $s\left(x,y\right)=\sqrt{u{\left(x,y\right)}^2+v{\left(x,y\right)}^2}$. Find $\frac{\partial s}{\partial x}$ and $\frac{\partial s}{\partial y}$ using the chain rule.