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1. Determine an expression for dy/dt if x^2+2y^2=8 and dx/dt=3.

2. A point is moving along the right branch of a hyperbola defined by 4x^2-y^2=64. What is dy/dt when the point is at (5, -6) and dx/dt=3?

I will start you on the first, using implicit differention.

2x dx/dt + 4ydy/dt=0
solve for dy/dt

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