If x^2 + y^2 + z^2 = 9, dx/dt = 6, and dy/dt = 9, find dz/dt when (x, y, z) = (2, 2, 1). I know this is a related rates problem. According to what I know about related rates, the process should be 2*(dx/dt) + 2*(dy/dt) + 2*(dz/dt) = 0, and plugging in values given means its 2*6 + 2*9 + 2*(dz/dt) = 0. Cool, so add 12 and 18 together and subtract from both sides and divide by 2 to get dz/dt = -15. I don't understand why this answer is wrong, and I also don't understand why the problem gave me what x, y, and z equal when I can't figure out how it matters.