You mean that the question would be asking for
\(\displaystyle \frac{\partial f}{\partial y}\) or \(\displaystyle \frac{\partial f}{\partial x}\)
If this is the case, the question should be written as
Given that \(\displaystyle f(x,y) = 400000 + \sqrt{x} \sin 3y - x^3 y^5\), find \(\displaystyle \frac{\partial f}{\partial x}\) or even \(\displaystyle \frac{df}{dx}\).
But it was not. It is so clear that it is an implicit differentiation question.
Even if we assume that it is not an implicit differentiation question, \(\displaystyle \frac{dy}{dx}\), doesn't imply to treat \(\displaystyle y\) as a constant.
