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Calculus

Differentiation, Chain Rule

jee_main_2026_jan_21_shift_1

Grade None

Question:

The derivative of y = sin(e^{2x}) at x = 0 is:

A. 2

B. 2 cos 1

C. cos 1

D. 2e

Step-by-Step Solution

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

Step 1: u = e^{2x}. dy/dx = cos(e^{2x}) × 2e^{2x}. Step 2: At x = 0, dy/dx = cos(1) × 2 = 2 cos 1.

Correct Answer: B

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