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Home Q & A Board Science-Related Homework Help Mathematics
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juju juju
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11 years ago
I understand the concept of implicit differentiation but this problem is giving me hell.
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wrote...
#1
11 years ago
y=(-3x-5)/4 i think
wrote...
#2
11 years ago
simple

expand it

2 (x^2) y + 3 x y ^2 =2

d/dx both sides

2 y (2x) + 2 x^2  dy/dx   + 3 y ^2 + 3 x (2y dy/dx) = 0

3 y^2 + 4 xy + ( 2 x^2 + 6 xy) dy/dx =0
wrote...
#3
11 years ago
xy(2x+3y)=2
2x²y + 3xy² = 2

Differentiate 2x²y using the product rule to get:
2x²dy/dx + 4xy

Differentiate 3xy² using the product rule to get:
6xydy/dx + 3y²

The derivative of the constant, 2, is 0.

Put this together to get:
2x²dy/dx + 4xy + 6xydy/dx + 3y² = 0
2x²dy/dx + 6xydy/dx = -(4xy+3y²)
Factorise:
2x(x+3y)dy/dx = -y(4x+3y)
dy/dx = -y(4x+3y)/2x(x+3y)

I hope this helps.
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