06 種々の関数の微分演習

本時の目標

  1. 種々の関数について導関数をスムーズに求めることができる。

課題1 次の関数を微分しましょう。

  1. \(\displaystyle f(x) = (x + 1)(x^2 - x + 1)\) 解答 隠す
  2. \(\displaystyle f(x) = (x^2 + 2x - 3)^3\) 解答 隠す
  3. \(\displaystyle f(x) = (x - 1)^2(x + 1)^3\) 解答 隠す
  4. \(\displaystyle f(x) = x(x - 1)(x - 2)\) 解答 隠す
  5. \(\displaystyle f(x) = \left(\frac{x}{x - 1}\right)^2\) 解答 隠す
  6. \(\displaystyle f(x) = \left(2 - \frac{1}{x}\right)^3\) 解答 隠す
  7. \(\displaystyle f(x) = \frac{x - 1}{x^2 + x + 1}\) 解答 隠す
  8. \(\displaystyle f(x) = \frac{x}{(x + 2)^2}\) 解答 隠す
  9. \(\displaystyle f(x) = \frac{x}{\sqrt{x^2 + 1}}\) 解答 隠す
  10. \(\displaystyle f(x) = \sqrt[3]{2x^2 - 3}\) 解答 隠す
  11. \(\displaystyle f(x) = \sqrt[4]{(3x^2 + 2x + 1)^3}\) 解答 隠す
  12. \(\displaystyle f(x) = \sqrt{\frac{1 - x}{1 + x}}\) 解答 隠す
  13. \(\displaystyle f(x) = \sin^2 x\) 解答 隠す
  14. \(\displaystyle f(x) = \cos^3 2x\) 解答 隠す
  15. \(\displaystyle f(x) = \sqrt{\sin^2 x + 1}\) 解答 隠す
  16. \(\displaystyle f(x) = \sin^2 x \cos 2x\) 解答 隠す
  17. \(\displaystyle f(x) = \log |\,x\,|\) 解答 隠す
  18. \(\displaystyle f(x) = e^x + e^{-x}\) 解答 隠す
  19. \(\displaystyle f(x) = \log |\,\sin x\,|\) 解答 隠す
  20. \(\displaystyle f(x) = (x^2 + x + 1)e^{2x}\) 解答 隠す
  21. \(\displaystyle f(x) = \log\left(\log x\right)\) 解答 隠す
  22. \(\displaystyle f(x) = e^{-2x}\cos 2x\) 解答 隠す
  23. \(\displaystyle f(x) = \log \sqrt{\frac{x + 1}{x - 1}}\) 解答 隠す
  24. \(\displaystyle f(x) = \frac{e^{x^2}}{x}\) 解答 隠す
  25. \(\displaystyle f(x) = \log\left(x + \sqrt{x^2 + 1}\right)\) 解答 隠す
Last modified: Friday, 5 March 2021, 5:01 PM