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If x2 + y2 + z2 = 9, dxdt = 4, and dydt = 8, find dzdt when (x, y, z) = (2, 2, 1).

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If x2 + y2 + z2 = 9, dxdt = 4, and dydt = 8, find dzdt when (x, y, z) = (2, 2, 1).
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Solution 1

To solve this problem, we need to use the chain rule of differentiation.

Given the equation x² + y² + z² = 9, we can differentiate both sides with respect to t to get:

2x(dx/dt) + 2y(dy/dt) + 2z(dz/dt) = 0.

We know that dx/dt = 4, dy/dt = 8, and we are trying to find dz/dt. We also know that at Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.

Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
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