Which one is the variable? (Derivatives)

Standard or common notation would have $c$ be the constant, and $\theta$ the variable.

In Calc I, early letters ($a, b, c, d \ldots$) are ususally constants, and late letters ($x, y, z$) are usually variables. $\theta$ is often used for a variable when the variable in question is an angle, just as $t$ is used for time, or $r$ for a radial distance.

In strict terms, this is ambiguous. This may be $y(\theta)$ or $y(c)$; in each case the other variable is fixed. However, as noted, the likely intended interpretation is that $\theta$ is the variable.

The correct answer is:

O Questioner, differentiate with respect to what???

Do you want $\frac{dy}{dc}$ or $\frac{dy}{dθ}$? Or perhaps $\frac{dθ}{dc}$?