Question:
If \(z=x^2-y^2\), then
\[
\frac{1}{x}\frac{\partial z}{\partial x}+
\frac{1}{y}\frac{\partial z}{\partial y}
=
\]
If \(z=x^2-y^2\), then
\[
\frac{1}{x}\frac{\partial z}{\partial x}+
\frac{1}{y}\frac{\partial z}{\partial y}
=
\]
Show Hint
In partial differentiation, treat other variables as constants.
Updated On: May 27, 2026
- \(1\)
- \(2x+2y\)
- \(0\)
- \(2x-2y\)
Show Solution
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The Correct Option is C
Solution and Explanation
Step 1: Given: \[ z=x^2-y^2 \]
Step 2: \[ \frac{\partial z}{\partial x}=2x \] \[ \frac{\partial z}{\partial y}=-2y \]
Step 3: Substitute: \[ \frac{1}{x}(2x)+\frac{1}{y}(-2y) \] \[ =2-2 \] \[ =0 \] \[ \boxed{0} \]
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