If $x ^ { 2 } + 3 x y + y ^ { 2 } = 15$ , then $\frac { d y } { d x } = 2 x + 3 y$

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By implicit differentiation, we have:$$\frac{d}{dx}(x^2 + 3xy + y^2) = \frac{d}{dx}(15)$$$$2x + 3y\frac{dy}{dx} + 2y\frac{dy}{dx} = 0$$$$2x + 3y\frac{dy}{dx} + 2y\frac{dy}{dx} = 0$$$$\frac{dy}{dx} = \frac{-2x}{3y + 2y} = \frac{-2x}{5y} = \frac{-2x}{5y} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy}{dx} = \frac{-2x}{5y}$$$$\frac{dy

If x2+3xy+y2=15x ^ { 2 } + 3 x y + y ^ { 2 } = 15x2+3xy+y2=15

If $x ^ { 2 } + 3 x y + y ^ { 2 } = 15$