Questions: Introduction to differentiation and the derivative
Before attempting these questions, it is highly recommended that you read Guide: Introduction to differentiation and the derivative.
In this guide, the following definitions are used:
\[\cosh(x) = \frac{e^{x} + e^{-x}}{2} \quad\textsf{ and }\quad \sinh(x) = \frac{e^{x} - e^{-x}}{2}\] These are hyperbolic trigonometric functions; for more about these, see [Guide: Introduction to hyperbolic functions].
Using the differentiation rules seen in Guide: Introduction to differentiation and the derivative, differentiate the following functions:
1.1. \(\quad x^3+5x - 3\)
1.2. \(\quad 5x\)
1.3. \(\quad -5\sqrt{x}\)
1.4. \(\quad -\sin(x)\)
1.5. \(\quad \cos(x) + 5\)
1.6. \(\quad 2\sqrt{x}\)
1.7. \(\quad 2\ln(2x) + x^5\)
1.8. \(\quad \ln(5x)\)
1.9. \(\quad e^{-x}\)
1.10. \(\quad 23x + 5\)
1.11. \(\quad 4x + 100\)
1.12. \(\quad \sinh(5x)\)
1.13 \(\quad \cos(3x) - \sin(2x)\)
1.14 \(\quad \ln(x) +\cos(x) + 3x\)
1.15. \(\displaystyle\quad \frac{2}{5}\sinh(x) + \frac{2}{13}\cosh(x)\)
1.16. \(\quad e^{5x} + x^2 + 3\)
1.17. \(\quad \ln(x) + x^2\)
1.18. \(\quad \ln(5x) - \ln(x)\)
1.19. \(\quad \cosh(x) -5x^7\)
1.20. \(\quad \sqrt{3x^2}\)
1.21. \(\quad x^3 + 3x - \sqrt{2x}\)
After attempting the questions above, please click this link to find the answers.
Version history and licensing
v1.0: initial version created 03/25 by Sara Delgado Garcia as part of a University of St Andrews VIP project.