Originally Posted by

**TheMathTham** The exact wording of the problem is: "Determine the slope of the normal line to the curve $\displaystyle x^{3}+xy^{2} = 10y$ at the point $\displaystyle (2,1)$"

Now since finding the slope is the same thing as finding the derivative, I assumed that I would need to take the derivative of the problem, aka use implicit differentiation.

I got: $\displaystyle 3x^{2}+ {\color{red}y^{2}y{}'} +x2yy{}' = 10y{}'$ Mr F says: The red term is wrong.

Which would mean that $\displaystyle \frac{\mathrm{dy} }{\mathrm{d} x}=\frac{3x^{2}}{-y^{2}-x2y+10}$

However, when I plugged in$\displaystyle x$ and $\displaystyle y$, I got $\displaystyle \frac{12}{5}$, which was not among the answer choices of $\displaystyle 0$,$\displaystyle 2$,$\displaystyle -\frac{7}{3}$,$\displaystyle -\frac{6}{13}$, or $\displaystyle \frac{1}{2}$.