5.1 Using the appropriate properties of ordinary derivatives, perform the following.
(a) Find all the first partial derivatives of the following functions f(x, y):
(i) x2y, (ii) x2 + y2 + 4, (iii) sin(x/y), (iv) tan–1(y/x),
(v) r(x, y, z) = (x2 + y2 + z2)1/2.
(b) For (i), (ii) and (v), find ∂2f/∂x2, ∂2f/∂y2 and ∂2f/∂x∂y.
(c) For (iv) verify that ∂2f/∂x∂y = ∂2f/∂y∂x.
These are all straightforward applications of the ...