Question

Suppose that f(x) is a function of one variable whose second derivative
exists and put u(x, t) = f(x + ct), where c is some positive number.
Determine the following partial derivatives in terms of f and its deriva-
tives: (let d = partial derivative)
du/dx; du/dt; d^2u/dx^2; d^2u/dt^2; d^2u/dxdt

Answer 1

Recall that u is related to a wave whose prole is the graph of f and
travelling with speed c.