Questions: The chain rule
Before attempting these questions, it is highly recommended that you read Guide: The chain rule..
Differentiate the following functions using the chain rule.
1.1. \(\quad \dfrac{1}{7}\cos(5+4x)\)
1.2. \(\quad 4\cos(x^2)\)
1.3. \(\quad e^{x^2 + 5}\)
1.4. \(\quad 2(\sin(2x))^2\)
1.5. \(\quad e^{\sin(3x)}\)
1.6. \(\quad \ln({{2+ 4x^{-2}})^{-1}}\)
1.7. \(\quad e^{5x^4}\) changed
1.8. \(\quad e^{2x^{-3}}\) changed
1.9. \(\quad -5\sqrt{x-2}\)
1.10. \(\quad \sqrt{(x+3)^2}\)
1.11. \(\quad \ln (x^2 +1)\)
1.12. \(\quad \ln(\cos(x))\).
1.13. \(\quad 2\cos^2(x)\).
1.14. \(\quad 2(x^3 + 5x^2 + 13x -1)^3\).
1.15. \(\quad \sqrt{\dfrac{1}{2x}}\).
1.16. \(\quad \cos(5x^{-1/2})\). changed
1.17. \(\quad \sin\left(\sqrt{x^2+1}\right)\)
1.18. \(\quad \sin(e^x)\)
1.19. \(\quad \cos(e^{-2x} + 5)\)
1.20. \(\quad \ln(3x^3 + \sin(x))\)
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.