If x, y, and z are lengths of the edges of a rectangular box, the common length of the box’s diagonals is s = √x² + y² + z².

a. Assuming that x, y, and z are differentiable functions of t, how is ds/dt related to dx/dt, dy/dt, and dz/dt?

b. How is ds/dt related to dy/dt and dz/dt if x is constant?

c. How are dx/dt, dy/dt, and dz/dt related if s is constant?