Questions: The chain rule

Author

Sara Delgado Garcia

Summary
A selection of questions for the study guide on 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.

This work is licensed under CC BY-NC-SA 4.0.

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