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Find an equation of the line tangent to 2x^2-x-ln(x-4)-y^2=9 at (5,6)

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differentiate implicitly

4x - 1 - 1/(x-4) - 2ydy/dx = 0

plug in (5,6) to get the slope which is dy/dx

Now you are back to a simple grade 9 problem of finding the equation of a straight line given the slope and a point

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