math Use implicit differentiation if y= x^2-5xy+3y^2=7

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To find the derivative dy/dx of y= x^2-5xy+3y^2 implicit differentiation can be used and differentiation carried out in the following way:

y= x^2-5xy+3y^2

dy/dx = 2x - 5*x*(dy/dx) - 5y + 6y*(dy/dx)

take all terms with dy/dx to one side

dy/dx + 5*x*(dy/dx) - 6y*(dy/dx) = 2x - 5y

=> dy/dx( 1 + 5x - 6y) = 2x - 5y

=> dy/dx = (2x - 5y)/(1 + 5x - 6y)

The derivative dy/dx = (2x - 5y)/(1 + 5x - 6y)

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