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

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