JEE (Main) Mathematics - Differentiation Questions (31 to 45)

What is the derivative of sin x?
- A) cos x
- B) -cos x
- C) sin x
- D) -sin x
Answer: A) cos x
What is the derivative of tan x?
- A) sec² x
- B) cos² x
- C) sin² x
- D) sec x
Answer: A) sec² x
What is the derivative of ln x?
- A) 1/x
- B) x
- C) ln x
- D) 1/x²
Answer: A) 1/x
What is the derivative of e^x?
- A) e^x
- B) x * e^x
- C) 1/e^x
- D) e^x + 1
Answer: A) e^x
What is the derivative of arcsin x?
- A) 1 / √(1 - x²)
- B) 1 / √(1 + x²)
- C) 1 / √(x² - 1)
- D) √(1 - x²)
Answer: A) 1 / √(1 - x²)
What is the derivative of arccos x?
- A) -1 / √(1 - x²)
- B) 1 / √(1 - x²)
- C) -1 / √(1 + x²)
- D) 1 / √(x² - 1)
Answer: A) -1 / √(1 - x²)
What is the derivative of xⁿ (where n is a constant)?
- A) nxⁿ⁻¹
- B) nxⁿ
- C) nˣ
- D) xⁿ⁺¹
Answer: A) nxⁿ⁻¹
What is the derivative of ln x²?
- A) 2 / x
- B) 1 / x²
- C) 2 / x²
- D) 1 / x
Answer: A) 2 / x
What is the second derivative of sin x?
- A) -sin x
- B) cos x
- C) -cos x
- D) sin x
Answer: C) -cos x
The second derivative of f(x) = x³ - 3x + 2 is:
- A) 6x
- B) 6x - 3
- C) 6x² - 6
- D) 6x²
Answer: D) 6x²
What is the derivative of 1/x?
- A) -1 / x²
- B) 1 / x²
- C) -1 / x
- D) -x
Answer: A) -1 / x²
The derivative of cot x is:
- A) -csc² x
- B) sec² x
- C) csc² x
- D) -sec² x
Answer: A) -csc² x
The derivative of tan⁻¹ x is:
- A) 1 / (1 + x²)
- B) 1 / (1 - x²)
- C) 1 / (x² + 1)
- D) 1 / √(1 - x²)
Answer: A) 1 / (1 + x²)
The derivative of the function f(x) = sin x + cos x is:
- A) cos x - sin x
- B) cos x + sin x
- C) -cos x - sin x
- D) -sin x + cos x
Answer: A) cos x - sin x
The derivative of ln(x² + 1) is:
- A) 2x / (x² + 1)
- B) x / (x² + 1)
- C) 1 / (x² + 1)
- D) 2 / (x² + 1)
Answer: A) 2x / (x² + 1)

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JEE (Main) Mathematics - Differentiation Questions (31 to 45)

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