Assuming that each equation in problems 1-12 defines a differentiable function of x, find Dxy by implicit differentiation.
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Y2 – x2 = 1
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9x2 + 4y2 = 36
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xy = 1
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X2 + 2y2 = 4 2, where is a constant.
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Xy2 = x – 8
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X2 + 2x2y + 3xy = 0
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4x3 + 7xy2 = 2y3
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X2y = 1 + y2x
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+ 2y = y2 + xy3
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x + 2y = y2 + xy3
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xy + sin(xy) = 1
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cos(xy2) = y2 + x
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e2x+3y = x2 – ln(xy3)
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x2tan(y) + y10sec(x) = 2x
in problems 15-20, find the equation of the tangent line at the indicated point.
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X3y + y3x = 30; (1 , 3)
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X2y2 + 4xy = 12y; (2 , 1)
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Sin(xy) = y; (π/2 , 1)
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y + cos(xy2) + 3x2 = 4; (1 , 0)
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x2/3 – y2/3 – 2y = 2; (1 , -1)
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√x + xy2 = 5; (4 , 1)
In problems 21-32, find dy/dx
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y = 3x5/3 +
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y = ∛x – 2x7/2
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y = ∛x + √x
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y = ∜(2x + 1)
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y = ∜(3x2 - 4x)
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y = (x3 – 2x )1/3
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y = 1 / (x3 + 2x)2/3
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y = (3x – 9)-5/3
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y = √(x2 + sinx)
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y = √(x2cosx )
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y = 1 / (∛(x2sinx))
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y = ∜(1 + sin5x)