Differentiation Jamb Mathematics Past Questions
Question 1
If \(y = 6x^3 + 2x^{-2} - x^{-3}\), find \(\frac{\mathrm d y}{\mathrm d x}\).
- A. \(\frac{\mathrm d y}{\mathrm d x} = 15x^2 - 4x^{-2} - 3x^{-2}\)
- B. \(\frac{\mathrm d y}{\mathrm d x} = 6x + 4x^{-1} - 3x^{-4}\)
- C. \(\frac{\mathrm d y}{\mathrm d x} = 18x^2 - 4x^{-3} + 3x^{-4}\)
- D. \(\frac{\mathrm d y}{\mathrm d x} = 12x^2 + 4x^{-1} - 3x^{-2}\)
Question 2
\(\frac{d}{dx} [\log (4x^3 - 2x)]\) is equal to
- A. \(\frac{12x - 2}{4x^2}\)
- B. \(\frac{43x^2 - 2x}{7x}\)
- C. \(\frac{4x^2 - 2}{7x + 6}\)
- D. \(\frac{12x^2 - 2}{4x^3 - 2x}\)
Question 3
If S = (4t + 3)(t - 2), find ds/dt when t = 5 secs.
- A. 50 units per sec
- B. 35 units per sec
- C. 22 units per sec
- D. 13 units per sec
Question 4
What is the derivative of \(t^2\) sin (3t - 5) with respect to t?
- A. 6t cos (3t - 5)
- B. 2t sin (3t - 5) - 3\(t^2\) cos (3t - 5)
- C. 2t sin (3t - 5) + 3\(t^2\) cos (3t - 5)
- D. 2t sin (3t - 5) + \(t^2\) cos 3t
Question 5
Simplify \(\frac{3(2^{n+1}) - 4(2^{n-1})}{2^{n+1} - 2^n}\)
- A. 2n+1
- B. 2n-1
- C. 4
- D. 1/4
