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SSC Pure Mathematics QUESTION #1280
Question 1
If \(w=f(x^2+y^2)\), then the expression \(y\dfrac{\partial w}{\partial x}-x\dfrac{\partial w}{\partial y}\) equals:
  • 1
  • \(2xy\)
  • \(f'(x^2+y^2)\)
Correct Answer Explanation
Let \(t=x^2+y^2\). Then \(\dfrac{\partial w}{\partial x}=f'(t)\cdot2x\) and \(\dfrac{\partial w}{\partial y}=f'(t)\cdot2y\). So: \(y\dfrac{\partial w}{\partial x}-x\dfrac{\partial w}{\partial y}=y\cdot2xf'(t)-x\cdot2yf'(t)=2xyf'(t)-2xyf'(t)=0\).