Question Find $y'$ given $\sin(x) = e^y$, where options are $-\tan(x)$, $\tan(x)$, $\cot(x)$, $-\cot(x)$.

Studdy Solution
Since $\cot(x)$ is positive when $\sin(x)$ is positive and negative when $\sin(x)$ is negative (in the respective quadrants), our earlier expression for $\frac{dy}{dx}$ is correct.
$$\frac{dy}{dx} = \cot(x)$$
Thus, the correct answer is c. $\cot(x)$.