APFIVE Implicit Differentiation with Product Rule
For the equation $$x^2*y + e^y = x$$, use implicit differentiation (without using a calculator) to determine which of the following equations correctly represents $$\frac{dy}{dx}$$ in terms of x and y.
| x | y |
|---|---|
| 1 | 0 |
| 2 | ? |
A
$$\frac{1-2*x*y}{x^2+e^y}$$
B
$$\frac{1+2*x*y}{x^2+e^y}$$
C
$$\frac{1-2*x*y}{x^2-e^y}$$
D
$$\frac{2*x*y-1}{x^2+e^y}$$
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