For f(x,y)=x2y+3y2x, evaluate 2f/ x2 at (1,1).

GATE 2026 BM – Question 17

Engineering Mathematics · Calculus · 1 mark · Multiple choice

For $f(x,y)=x^2y+3y^2x$, evaluate $\partial^2f/\partial x^2$ at (1,1).

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) 2

Explanation

Hold y constant when differentiating with respect to x. The first derivative is 2xy+3y², and the second is 2y. At y=1 this becomes two, independently of x, so C.

More Calculus questions

GATE 2026 BM Q40 – For f(x,y)=x2+y2, evaluate PQ f d l along the quarter-unit-circle path shown, from P=(1,0)…
GATE 2025 BM Q18 – A real function f is continuous and differentiable with f′(x)≠0 everywhere. For finite…
GATE 2025 BM Q32 – For f(x)=x-1/x, evaluate x0[f(1+ x)-f(1)]/ x.
GATE 2024 BM Q50 – For F=(x+y) i+(x+y) j, evaluate F d r counterclockwise around the unit square…
GATE 2023 BM Q15 – For f(x,y)=ex y, evaluate 2 f/( x y) at x=0,y=/2.
GATE 2023 BM Q53 – For f(x)=x⁴−x² on the real line, which statements are correct?

All Calculus questions →