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Find dy/dx by implicit differentiation. 4x2 + 5xy - y2 = 6
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Find dy/dx by implicit differentiation.
4x2 + 5xy - y2 = 6

User Jacek Lampart
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1 Answer

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4x^2 + 5xy - y^2 = 6
Implicitly differentiating both sides,
4(2x) + 5(x y' + y) - 2yy' = 0

where y' = dy/dx

8x + 5xy' +5y -2yy' = 0

combining y' terms
y' (5x-2y) +8x +5y = 0

y'(5x-2y) = -(8x+5y)

dy/dx = -(8x+5y)/(5x-2y)
or
dy/dx = (8x+5y)/(2y-5x)
User System Down
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