Find dxdy if x−y=π.
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Step-by-Step Solution
Step 1: Differentiate both sides with respect to x
To find dxdy, we need to differentiate both sides of the given equation x−y=π 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 dxdy. The derivative of a constant, π, 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 dxdy, and the derivative of π (a constant) is 0.
Step 4: Solve for dxdy
To isolate dxdy, we can rearrange the equation. Adding dxdy to both sides gives us 1=dxdy.