hope this'll help you
then
Q: Point A moves along the x-axis at the constant rate of 8ft/sec while point B moves along the y-axis at the constant rate of 10ft/sec. Find how fast the distance between them is changing when A is at the point (10,0) and B is at the point (0,8).
z^2 = x^2 + y^2
x = 10
y = 8
z = sqrt(10^2 + 8^2) --> sqrt(164)
x' = 8
y' = 10
want to find z'
2z*dz/dt = 2x*dx/dt + 2y^dy/dt
dz/dt = [2x(dx/dt) + 2y(dy/dt)] / 2z
dz/dt = [2*8*10 + 2*8*10] / 2z
dz/dt = 320 / 2z
dz/dt = 160 / sqrt(164) --> FINAL ANSWER!
OK, using that i redid the problem and got:
z^2 = x^2 + y^2
x = 10
y = 8
z = sqrt(10^2 + 8^2) --> sqrt(164)
x' = 8
y' = 10
want to find z'
2z(dz/dt) = 2x(dx/dt) + 2y(dy/dt)
dz/dt = [2x(dx/dt) + 2y(dy/dt)] / 2z
dz/dt = [2*8*10 + 2*8*10] / 2z
dz/dt = 320 / 2z
dz/dt = 160 / sqrt(164) --> FINAL ANSWER!