Question

If \(x-y=\pi\), then the value of \(\dfrac{dy}{dx}\) is:

• A. 0
• B. \(\pi\)
• C. 1
• D. \(x\)

Hint:

Differentiate x - y = constant directly; the derivative of a constant is 0.

Answer 1

The Correct Option is C

Step 1: Rewrite as \(y=x-\pi\):
Since $\pi$ is just a constant, solve explicitly for $y$: $y=x-\pi$.

Step 2: Differentiate directly:
$\dfrac{dy}{dx}=\dfrac{d}{dx}(x)-\dfrac{d}{dx}(\pi)=1-0=1$.

Final Answer:
\[ \boxed{\dfrac{dy}{dx}=1} \]