GATE 2023 PI – Question 36
$z(x,y)=e^{x-2y}$, $x(t)=e^t$, $y(t)=e^{-t}$, with all variables real. Find dz/dt.
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Correct answer: (C) $z(x+2y)$
Explanation
The chain rule gives $dz/dt=z(dx/dt-2dy/dt)$. Since dx/dt = x and dy/dt = −y, the result is **z(x+2y), C**.