For f(x,y)=ex y, evaluate 2 f/( x y) at x=0,y=/2.

GATE 2023 BM – Question 15

Engineering Mathematics · Calculus · 1 mark · Multiple choice

For $f(x,y)=e^x\cos y$, evaluate $\partial^2 f/(\partial x\partial y)$ at $x=0,y=\pi/2$.

0
1
−1
$e^{\pi/2}$

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Show answer and explanation

Correct answer: (C) −1

Explanation

Differentiating once with respect to y gives −eˣsin y, and then with respect to x leaves −eˣsin y. At x=0 and y=π/2, e⁰=1 and sin(π/2)=1, so the mixed derivative is −1, C.

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