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GATE 2026 MT – Question 13

Engineering Mathematics · Calculus and vector calculus · 1 mark · Multiple choice

Given $w=f(ax+by)$, where $a$ and $b$ are constants, the value of $b\frac{\partial w}{\partial x}-a\frac{\partial w}{\partial y}$ is ________.

  1. $-a$
  2. $b$
  3. $b-a$
  4. 0

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Correct answer: (D) 0

Explanation

Put $u=ax+by$. The chain rule gives $\partial w/\partial x=af\prime(u)$ and $\partial w/\partial y=bf\prime(u)$.

The requested combination is $abf\prime(u)-abf\prime(u)=0$. Hence **D**.