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Calculus

Differentiation, Chain Rule

jee_main_2026_jan_22_shift_1

Grade None

Question:

The derivative of y = sin(3x² + 2x) at x = 0 is:

A. 0

B. 1

C. 2

D. 3

Step-by-Step Solution

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

Step 1: u = 3x² + 2x. dy/dx = cos(3x²+2x) × (6x + 2). Step 2: At x = 0, dy/dx = cos 0 × 2 = 2.

Correct Answer: C

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