Calculus Question

Question

If  z^2=x^2+y^2,dx/dt=8,  and  dy/dt=5,  find  dz/dt  when  x=5  and  y=2

Answer 1

z² = x² + y² When x = 5 and y = 2, z² = 5² + 2² = 29. So, z = √29

2z(dz/dt) = 2x(dx/dt) + 2y(dy/dt)

2√29(dz/dt) = (10)(8) + (4)(5)

Solve for dz/dt.