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Calculus Drill on Derivatives!!!!!!!!!!

Calculus Drill on Derivatives!!!!!!!!!!. 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 Exam. When you think you know the answer,

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Calculus Drill on Derivatives!!!!!!!!!!

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  1. CalculusDrill on Derivatives!!!!!!!!!!

  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 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 your 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 challenging derivative!

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

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

  44. f ’(x)g(x) + f(x)g‘(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??

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

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

  47. d/dx(f(g(x))) Chain chain chain…. ♫ Chain of foooools! ♪ ♫ ♫

  48. Yeah yeah…you’re good now… But what about that Chain Rule? Don’t forget all three steps! • Derivative of outside • Copy inside • Multiply by the “derivative of inside”

  49. d/dx(y) Are you confused yet?

  50. dy/dx • Did I trick you ?

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