Show that under the hypotheses of Problem 1 one has[Hint: Use Problem 2.]Problem 1Prove th...

Show that under the hypotheses of Problem 1 one has

[Hint: Use Problem 2.]

Problem 1

Prove that if u = f(x, y) and v = g(x, y) are functions such that

then

for every angle α.

Problem 2

Show that if u = f(x, y), then the directional derivatives of u along the line θ = const and circles r = const (polar coordinates) are given respectively by