<s>[INST] Differentiation involving implicit and parametric. I was asked to differentiate the term, 
$$X^3 + XY^2  - Y^3$$
For such I reached,
$$3X^2 + 2XY\dfrac{dy}{dx}  - 3Y^2\dfrac{dy}{dx}$$
The apparent answer is,
$$3X^2 + Y^2 + 2XY\dfrac{dy}{dx} - 3Y^2\dfrac{dy}{dx}$$
How exactly this is reached as I am new to the whole implicit and parametric function. 
 [/INST] You forgot about the product rule. Assuming $y=y(x),$
\begin{align*}
\frac{d}{dx} \left( x^3 +xy^2 - y^3 \right) &= 3x^2 + \frac{d}{dx} \left(xy^2 \right) -3y^2 \frac{dy}{dx} \\
&= 3x^2 + 2xy \frac{dy}{dx} + y^2 - 3y^2 \frac{dy}{dx}
\end{align*}
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