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Calculus

Differentiation, Chain Rule

jee_main_2026_jan_22_shift_1

Grade None

Question:

The derivative of \(y = \cos(2x^2 + 3x)\) at \(x = 0\) is:

A. 0

B. -1

C. -2

D. -3

Step-by-Step Solution

Key Concept: Use chain rule: d/dx cos(u) = -sin u × du/dx.

Step 1: u = 2x² + 3x. dy/dx = -sin(2x²+3x) × (4x + 3). Step 2: At x = 0, dy/dx = -sin 0 × 3 = 0.

Correct Answer: A

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