GATE AG 2014 • Q13 NAT • 1 Mark

Section 1: Engineering Mathematics

Calculus

Subtopic: Partial derivatives

Question Statement:

If f(x,y) = 3x² − 4xy + 2y², the summation of ∂f/∂x and ∂f/∂y for x = 1 and y = 2 is _______.

Official Answer Key:

2 to 2

Step-by-Step Solution & Explanation

∂f/∂x = 6x − 4y; ∂f/∂y = −4x + 4y. At (x,y) = (1,2): ∂f/∂x = 6(1) − 4(2) = 6 − 8 = −2. ∂f/∂y = −4(1) + 4(2) = −4 + 8 = 4. Sum = −2 + 4 = 2.

Practice This in Real CBT Exam Interface

Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.

Launch CBT Mock Test