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Mastering Derivatives: Fun and Engaging Practice for AP Calculus AB

Dive into an interactive and lively derivative drill designed for AP Calculus AB students! This practice will help you memorize essential derivatives quickly, ensuring you're ready for the AP exam. Each derivative question prompts you to recall answers fast, testing your understanding while keeping the learning fun. You'll cover various derivative rules, including trigonometric, logarithmic, and the product/quotient rules. Get ready to enhance your calculus skills with this catchy, musical approach to learning derivatives!

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Mastering Derivatives: Fun and Engaging Practice for AP Calculus AB

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Presentation Transcript

  1. Calculus AB Drill on Derivatives!!!!!!!!!! Sing it ~ “Oh I, I will derive 

  2. Derivative Drill & Practice • I’m going to ask you to remember some derivatives. • It’s important to be fast as time is your enemy on the AP Exam. • When you think you know the answer, • (or if you give up ) click to get to the next slide to see if you were correct.

  3. What’s the definition of f ‘(c)?

  4. There’s 2 of them! You really need to know both of these thoroughly!

  5. What’s the definition of f ‘(x)? This is a bit different…instead of the limit being a number…it will be a function related to f(x)

  6. Got it?? Notice that in the second definition, the arrow points to the independent variable in the final answer.

  7. What does the derivative, f ‘(x) tell you about f(x)? (There are many answers… how many do you know?)

  8. Here’s a few: Slope of the curve Instantaneous rate of change in f(x) Rate of change If f(x) is position…then velocity If f(x) is velocity…then acceleration

  9. Now… Here come a series of questions concerning basic derivatives you should know very quickly!

  10. Ready?

  11. d/dx(sin(x)) = ?? • What’s your answer?

  12. cos(x) • Were you right? (click for next question)

  13. d/dx(mxn) • What’s your answer?

  14. mnxn-1 • Were you right? (click for next question)

  15. d/dx(ef(x)) • What is your answer?

  16. f ’(x) ef(x) • Were you right? (click for next question)

  17. d/dx(ln|x|) • What is your answer?

  18. 1/x • Were you right? (click for next question)

  19. d/dx(ax) • What’s yer answer…eh?

  20. (ln a) ax • Were you right? (click for next question) I dig this calculus stuff!!

  21. d/dx (logax) • What’s your answer?

  22. Aghh! Never can remember this one!!! • Do it this way: logax = ln x / ln a (ln a is just a constant) so the answer is: 1 --------- x ln a Ready?

  23. d/dx(cos x) • What’s your answer? (yeah yeah yeah…back to trig!)

  24. - sin x • Did you remember the “-” ?? Were you right? (click for next question)

  25. d/dx(tan x) • Answer it baby!!

  26. sec2x • Were you right? (click for next question)

  27. d/dx(cot x) • The ugly step sister!

  28. - csc2x • Ya ya ya!! • Were you right? (click for next question)

  29. d/dx(sec x) • I call this one the wart derivative!

  30. sec x tan x • Were you right? (click for next question) (It’s the TRIG family!!)

  31. d/dx(csc x) • Get ‘er done!!!

  32. - csc x cot x • I think there’s a pattern, eh? (click for next question)

  33. d/dx(ln f(x)) • Ready?

  34. f ‘ (x) / f(x) • Were you right? (click for next question)

  35. d/dx (af(x)) • Go go go go!!!!!

  36. (ln a) f ‘ (x) af(x) • Were you right? (click for next question) Hit that ball!!

  37. d/dx (tan-1x) • Oh yeah! Inverse trig mama!

  38. 1/(1+x2) • Were you right? (click for next question) It’s not raining is it?

  39. d/dx(sin-1x) • You can do this one in your sleep! • Right?

  40. Did ya get it?? • Let’s keep going!!!

  41. d/dx(cos-1x) • If you knew the last one, ya know this one…….right??

  42. Oh yeah!

  43. d/dx(sec-1x) • This one’s a bit harder….

  44. Dah dah!!! • Did you know that one??

  45. d/dx(|x|) • This one is a bit esoteric…

  46. If you knew it was B PROUD of ya!

  47. d/dx(f(x)g(x)) • It’s the Product Rule! • (don’t flush it!!!)

  48. f(x)g‘(x)+g(x)f ’(x) Yeah…I know you know it…but I’m afraid… Promise me you will remember to use the product rule every time you take the derivative of a product! OK??

  49. d/dx(f(x)/g(x)) • It’s the merry mighty Quotient Rule!!

  50. Pleeeezzze!Don’t get the numerator backwards.

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