Use Implicit Differentiation To Find The Slope Of

Anonymous

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Use implicit differentiation to find the slope of the tangent line to the curve xy^3+xy=8 at the point (4,1) m= ????

 

Answer No.1

ZenMaster

From: US
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Y3 + 3xy2 y1 + y + xy1 = 0 at point (4,1) 1 + 12 y1 + 1 + 4y1 = 0 16 y1 = -2 y1 = -1/8 = -0.125

Answer No.2

AmericanBrain

From: US
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Votes: 21
Xy^3+xy=8 x(y^3 + y) = 8 x * d/dx (y^3 + y) + (y^3 + y)dx/dx = 0 x * (3y^2 + 1) dy/dx + (y^3 + y) = 0 slope = dy/dx = -(y^3 + y)/(x*(3y^2+1) ) = - (1^3 + 1)/[ 4 * (3*1^2+1)] = -1/8

Answer No.3

GamerNewton

From: US
Posts: 37
Votes: 111
X2y^2 dy/dx + y^3 + x dy/dx +y = 0 slope dy/dx = m = (-y^3-y)/(x+2xy^2) so m at (4,1) = (-2)/(12) = -1/6

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