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

Step 1: Differentiate both sides with respect to x

To find $\frac{dy}{dx}$, we need to differentiate both sides of the given equation $x-y=\pi$ with respect to $x$. This allows us to apply differentiation rules to each term.

Step 2: Apply the difference rule of differentiation

Using the difference rule of differentiation, we can differentiate each term separately. The derivative of $x$ with respect to $x$ is $1$, and the derivative of $y$ with respect to $x$ is $\frac{dy}{dx}$. The derivative of a constant, $\pi$, is $0$.

Step 3: Substitute the derivatives

Now we substitute the derivatives of each term into the equation. The derivative of $x$ is $1$, the derivative of $y$ is $\frac{dy}{dx}$, and the derivative of $\pi$ (a constant) is $0$.

Step 4: Solve for $\frac{dy}{dx}$

To isolate $\frac{dy}{dx}$, we can rearrange the equation. Adding $\frac{dy}{dx}$ to both sides gives us $1 = \frac{dy}{dx}$.

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