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Lenka Lenka
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Posts: 37
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12 years ago
Hi guys I need to find the derivative of the implicit function, but i have to use implicit differentiation
6x^2+8xy+y^2=6
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wrote...
#1
12 years ago
6x^2+8xy+y^2=6

dy/dx=-2(3x+2y)/(4x+y)
wrote...
#2
12 years ago
You must put a dy/dx after you derive every y term

6x^2 + 8xy + y^2 = 6

12x + (8x)(1)dy/dx + 8y + (2y)dy/dx = 0  
(I used the product rule for the 8xy term)


12x + (8x)dy/dx + 8y + (2y)dy/dx = 0

(8x)dy/dx + (2y)dy/dx = -12x - 8y
(I subtracted 12 and 8y from both sides)

dy/dx(8x + 2y) = -12x - 8y
(I factored out the dy/dx)

dy/dx = (-12x - 8y)/(8x + 2y)
(divided both sides by 8x + 2y)

dy/dx = 4(-3x - 2y)/2(4x + y)
(factored)

dy/dx = 2(-3x -2y)/(4x + y)
wrote...
#3
12 years ago
See:
6x^2+8xy+y^2=6
12x+8y+8xy'+2y.y'=0
8xy'+2y.y'=-12x-8y
(8x+2y).y'=-4(3x+2y)
y'=-4(3x+2y)/(8x+2y)
y'=-4(3x+2y)/2(4x+y)
y'=-2(3x+2y)/(4x+y)
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