An equation is formed when two equal expressions. The correct option is D.
What is an equation?
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The differentiation of the equation can be done as,
x³ + 3x²y + y³ = 8
[tex]\dfrac{d}{dx}x^3 + \dfrac{d}{dx}(3x^2y) + \dfrac{d}{dx}y^3 = \dfrac{d}{dx}8\\\\\\3x^2 + 3(2xy+ \dfrac{dy}{dx}x^2)+3y^2\dfrac{dy}{dx} = 0\\\\\\x^2 + 2xy+ \dfrac{dy}{dx}x^2+y^2\dfrac{dy}{dx} = 0\\\\\\\dfrac{dy}{dx}x^2+y^2\dfrac{dy}{dx} =-x^2-2xy\\\\\\\dfrac{dy}{dx}(x^2+y^2)=-x^2-2xy\\\\\\\dfrac{dy}{dx} = \dfrac{-x^2-2xy}{x^2+y^2}\\\\\\\dfrac{dy}{dx} = -\dfrac{x^2+2xy}{x^2+y^2}[/tex]
Hence, the correct option is D.
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