Questions: The quotient rule
Before attempting these questions, it is highly recommended that you read Guide: The quotient rule..
Differentiate the following functions using the quotient rule.
1.1. \(\quad \dfrac{e^x}{x}\)
1.2. \(\quad \dfrac{e^{7x}}{x^5}\)
1.3. \(\quad \dfrac{\ln(x)}{x^2}\)
1.4. \(\quad \dfrac{e^{-x}}{x^2 +11x - 2}\)
1.5. \(\quad \dfrac{x^3 +5x -5}{x^2 +3}\)
1.6. \(\quad \dfrac{\cos(x)}{x^2 + 3x - 1}\)
1.7. \(\quad \dfrac{\tan(x)}{\cos(x)}\)
1.8. \(\quad \dfrac{\ln(3x)}{\ln(5) + x}\)
1.9. \(\quad \dfrac{x^2 +3x}{\cos(x)}\)
1.10. \(\quad \dfrac{\ln(x)}{x^3 + 3}\).
1.11. \(\quad \dfrac{5\tan(x)}{x}\).
1.12. \(\quad \dfrac{3x^7 - 27x^2+ 2\sqrt{x}}{x^2 + 1}\).
1.13. \(\quad \dfrac{e^{-3x}}{e^{2x}}\).
1.14. \(\quad \dfrac{e^3x^3}{e^x}\).
1.15. \(\quad \dfrac{x^5}{x^5 +1}\).
1.16. \(\quad \dfrac{\tan(x)}{\ln(x)}\).
1.17. \(\quad \dfrac{3\sin(x)}{\ln(x)}\)
1.18. \(\quad \dfrac{\tan(x) + 5x}{\sec(3x)}\)
After attempting the questions above, please click this link to find the answers.
Version history and licensing
v1.0: initial version created 05/25 by Sara Delgado Garcia as part of a University of St Andrews VIP project.