Question

If $x-y=\pi$, then $\dfrac{dy}{dx}$ is

• A. $\pi$
• B. $-\pi$
• C. $1$
• D. $-1$

Hint:

When differentiating equations involving constants, remember that the derivative of any constant is zero.

Answer 1

The Correct Option is C

Step 1: Write the given equation.
The relation between \(x\) and \(y\) is \[ x-y=\pi \] Here \(\pi\) is a constant.

Step 2: Differentiate both sides with respect to $x$.
\[ \frac{d}{dx}(x-y) = \frac{d}{dx}(\pi) \]
Step 3: Compute derivatives.
\[ \frac{d}{dx}(x)=1 \] \[ \frac{d}{dx}(y)=\frac{dy}{dx} \] Thus \[ 1-\frac{dy}{dx}=0 \]
Step 4: Solve for $\dfrac{dy{dx}$.

\[ \frac{dy}{dx}=1 \]
Step 5: Conclusion.
Hence the rate of change of \(y\) with respect to \(x\) is \(1\).
Final Answer: $\boxed{1}$