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FinFan FinFan
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12 years ago
How would you use implicit differentiation to find an equation of the tangent line to the curve

x^2+ 2xy-y^2+x=46 at the point (5,8)
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#1
12 years ago
differentiate
2x + 2y + 2xy' - 2yy' + 1 = 0 ----->y ' = 9/2 at (5,8)
equation of tangent
y - 8 = (9/2)(x - 5)
wrote...
#2
12 years ago
you plug in the numbers to the answer I get.

2x + 2( x dy /dx + y) - 2y dy / dx + 1 = 0
(2x - 2y) dy /dx + 2x + 2y + 1 = 0
dy / dx = -(2x + 2y + 1) / (2x - 2y)


whatever you get, put it in this expression:

y - y1 = m(x - x1)
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