Find $\frac{dy}{dx}$ if $x - y = \pi$.

$1$

The correct answer is Option (4) → 1 ##

Differentiating the relationship w.r.t., $x$, we have

$\frac{d}{dx}(x - y) = \frac{d\pi}{dx}$

Recall that $\frac{d\pi}{dx}$ means to differentiate the constant function taking value $\pi$ everywhere w.r.t., $x$. Thus

$\frac{d}{dx}(x) - \frac{d}{dx}(y) = 0$

which implies that

$\frac{dy}{dx} = \frac{dx}{dx} = 1$