5. If z = xyln(xy), then

(A) \(x \frac{\partial z }{\partial x} +y \frac{\partial z }{\partial y} =0\)

(B) \(y \frac{\partial z }{\partial x} =x \frac{\partial z }{\partial y} \)

(C) \(x \frac{\partial z }{\partial x} =y \frac{\partial z }{\partial y} \)

(D) \(y \frac{\partial z }{\partial x} +x \frac{\partial z }{\partial y} =0\)

Hint: 
Explanation: 

Answer-(C) \(x \frac{\partial z }{\partial x} =y \frac{\partial z }{\partial y} \)
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