GATE 2021 BM – Question 12

Engineering Mathematics · Calculus · 1 mark · Multiple choice

For $V(x,y)=(x^2+y^2)/2$, find its directional derivative at (1,1) in direction $3y\hat i-3x\hat j$.

√18
0
1/√18
3/2

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) 0

Explanation

The gradient is (x,y), hence (1,1) at the point. The direction vector there is (3,−3), whose unit vector is (1,−1)/√2. Their dot product is (1−1)/√2=0. Normalization does not affect this zero result. Thus B.

More Calculus questions

GATE 2021 BM Q31 – Find the minimum of f(x 1,x 2,x 3)=12(x 12+x 22+x 32)-2(x 1+x 2+x 3), rounded to the…
GATE 2020 BM Q19 – Which functions are odd? P=sin t, Q=cos t, R=sin t+cos t, S=sin t cos t.
GATE 2020 BM Q55 – Find the magnitude of the gradient of f(x,y)=x²+y² at (1,1), to two decimals.
GATE 2020 BM Q56 – Evaluate Rxy\,dx\,dy over the first-quadrant part of the unit disc, to three decimals.
GATE 2026 BM Q17 – For f(x,y)=x2y+3y2x, evaluate 2f/ x2 at (1,1).
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)…

All Calculus questions →