Question

Find dy/dx by implicit differentiation.
x7(x + y) = y2(2x − y)

Answer 1

\[x^7(x+y)+y^2(2x-4)\]?

Answer 2

\[\begin{align*}x^7(x+y)&=y^2(2x-y)\\
\frac{d}{dx}\left[x^7(x+y)\right]&=\frac{d}{dx}\left[y^2(2x-y)\right]\\
7x^6(x+y)+x^7\left(1+\frac{dy}{dx}\right)&=2y\frac{dy}{dx}(2x-y)+y^2\left(2-\frac{dy}{dx}\right)\\
7x^7+7x^6y+x^7+x^7\frac{dy}{dx}&=\left(4xy-2y^2\right)\frac{dy}{dx}+2y^2-y^2\frac{dy}{dx}\\
8x^7+7x^6y-2y^2&=\left(4xy-3y^2-x^7\right)\frac{dy}{dx}\\
\frac{dy}{dx}&=\cdots
\end{align*}\]