If y^2 + 3x^2 = 18, what is the slope of the tangent at the point (2, 6)

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The relation between x and y is `y^2 + 3x^2 = 18` . Use implicit differentiation to determine `dy/dx` .

`(d(y^2 + 3x^2))/(dx) = (d(18))/dx`

=> `2y*(dy/dx) + 6x = 0`

=> `dy/dx = (-6x)/(2y)`

=> `dy/dx = (-3x)/y`

At the point (2, 6) the value of `dy/dx = (-3*2)/6 = -1`

The slope of the tangent to the curve `y^2 + 3x^2 = 18` at (2, 6) is -1

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