The derivative of (sin x + cos x)² with respect to x is
Understanding the basics of calculus begins with CBSE 2024-2025 NCERT Maths Class 11th Chapter 12 Limits and Derivatives. This chapter introduces students to the concept of limits, which helps analyze the behavior of functions and derivatives, which measure the rate of change. MCQ questions in this chapter focus on evaluating limits using algebraic techniques, finding derivatives through first principles, and applying differentiation rules. Practicing these MCQs improves mathematical reasoning and problem-solving skills. A strong grasp of these topics is essential for higher studies in mathematics, physics and engineering. Regular practice of multiple-choice questions enhances accuracy and confidence, helping students prepare effectively for exams and future applications of calculus in various fields.
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Choice (b) is correct.
Let y = (sin x + cos x)² = sin² x + cos² x + 2 sin x cos x = 1 + 2 sin x cos x
dy/dx = d/dx (1 +2sin x cos x) = d/dx (1) + 2 d/dx (sin x cos x)
⇒ dy/dx = 0 + 2 ( sin x (d/dx) cos x + cos x(d/dx) sin x) = 2 {sin x (- sin x) + cos x (cos x)}
⇒dy/dx = 2(cos² x – sin² x) = 2 cos 2x
This question related to Chapter 12 maths Class 11th NCERT. From the Chapter 12: Limits and Derivatives. Give answer according to your understanding.
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