Chapter 14.6, Problem 2E

To determine

For the given function,

$\begin{array}{l}f(x,y)=x\cos (y)\\ x=u^2+y^2\\ y=u-v\end{array}$

(a) We have to determine primary derivatives.

$\frac{\partial f}{\partial x},\frac{\partial f}{\partial y}$

(b) By using chain rule to find $\frac{\partial f}{\partial v}$, answer should be in terms of both the dependent and independent variables.

(c) To find (x, y) for (u, v)= (2, 1) and evaluate $\frac{\partial f}{\partial v}$ at (u, v) = (2,1).