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# Implicit Differentiation

Not all equations can be written like y = f(x), so taking the derivative can be tricky. Save the mess and do it directly with implicit differentiation.

In a fairy tale, a wizard rides a cloud which is moving to the right at a speed of \(15\text{ m/s.}\) The wizard throws a ball vertically upward with a speed of \(3\text{ m/s}\) relative to the cloud. When the cloud has moved to the right \(30 \text{ m}\) following the throw, what is the velocity of the ball as seen by people on the ground?

Assume that air resistance is negligible and ignore the effect of gravity.

Note: The above diagram is not drawn to scale.

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