Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.

y = √x

(a) Find dy/dt, given x = 16 and dx/dt = 7.

dy/dt =

(b) Find dx/dt, given x = 64 and dy/dt = 8.

dx/dt =

... ?

This problem requires the use of the chain rule: dy / dt = [dy / dx] * [dx / dt]

y = √x = > dy / dx = 1 / (2√x)

(a) Find dy/dt, given x = 16 and dx/dt = 7.

dy/dt = [ 1 / (2√x) ] * 7 = [1 / (2*4) ] * 7 = 7/8

(b) Find dx/dt, given x = 64 and dy/dt = 8.

dx/dt = [dy/dt] / [dy/dx] = 8 / [1 / (2√64) ] = 128