GATE 2014 EC (EC4) – Question 15
Find the directional derivative of $f(x,y)=\frac{xy}{\sqrt2}(x+y)$ at (1,1), in the unit-vector direction making angle $\pi/4$ with the y-axis.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 2.99 to 3.01
Explanation
For f=xy(x+y)/√2, the partial derivatives at(1,1)are both3/√2. Taking the intended first-quadrant unit direction at45°to the y-axis gives u=(1/√2,1/√2). Their dot product is3/2+3/2=**3**. The angle alone needs a quadrant convention; the official key uses this positive direction.