Compute the following partial derivatives in the most efficient way

Question

Let

g(u,v,w)=eu4+v/1+u2 sin(u+3v)+u2 cos w/2

Compute the following partial derivatives in the most efficient way

(a) guv

(b) gvuu − guuv

Answer 1

(a) The function g is the sum of two terms and we can observe that the first term does not depend on w at all. It will therefore disappear, when we take the w-derivative. Thus we comput

(b) In this case we don’t have to do any computations at all, since

gvuu − guuv = 0 ,

because of the equality of mixed partial derivatives.