Find the indicated rate given he other information. x^2-8xy-y^2=129; dy/dt=6 when x=-1 and y=-8; find dx/dt.

Implicit Differentiation in terms of t. Please Help ME!

Differentiate with respect to t:
2x dx/dt - 8(x dy/dt + y dx/dt) - 2y dy/dt = 0.
∴ (2x - 8y) dx/dt = (8x + 2y) dy/dt.
∴ dx/dt = ((4x + y)/(x - 4y)) dy/dt.

Substituting x = -1, y = -8, and dy/dt = 6:
dx/dt = ((-4 - 8)/(-1 + 32)) * 6
= (-12/31) * 6
= -72/31.

No problem.

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