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Use implication differentiation to find dy/dx given 3y^2+xy=x^3+10

User Sascha Gehlich
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1 Answer

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14 votes

3y^2 +xy = x^3 + 10

Treat y as a function of x and take the derivative of each side with respect to x

3 * 2y ( dy/dx) + x * dy /dx + y *1 = 3x^2 + 0

6y dy /dx + x dy/dx +y = 3x^2

Subtract y

6y dy/dx + x dy/dx = 3x^2 -y

Factor out the dy/dx

dy/dx ( 6y +x) = 3x^2 -y

Divide by (6y+x)

dy/dx = ( 3x^2 -y)/ (6y+x)

User Clay Ellis
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