related Rates calculus

Question

Find dz/dt at (x,y)=(1,3) and z^2=x^2+y^2 if dx/dt=4 and dy/dt=3

Answer 1

dz/dt = 10/sqr13 = about 2.77

(x,y) = (1,3)

z^2 = x^2 + y^2 = 1^2 + 3^2 = 10

z = sqr10

x'= dx/dt = 4, y' dy/dt =3

2zz' = 2xx' +2yy'

zz' = xx' + yy' = 1(4) + 3(3) = 13

z' = dz/dt = 13/z = 13/sqr10 = about 2.77