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Fun With derivatives

By: Jennifer Larson. Fun With derivatives. START !. I’ve used this program before. I’m a first time user. WELCOME!.

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Fun With derivatives

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  1. By: Jennifer Larson Fun With derivatives START!

  2. I’ve used this program before I’m a first time user

  3. WELCOME! This program was designed to give students like you a fun way to learn calculus! Navigate through the program by clicking the icons at the bottom, left-hand corner of the screen! Home Next Back

  4. What do you want to learn? Pre-derivative review Definition of a derivative Derivative of a constant Power rule Sum rule Difference rule quiz

  5. Review Start!

  6. Remember… Slope=m= y2-y1 = y x2-x1 = x xmxn=xm+n xm = xm-n xn (xm)n = xmn x-n = 1 xn

  7. What is a Derivative? Find Out!

  8. We have all heard of a common form of a derivative…. slope!!

  9. Derivative- how much a quantity is changing at some given point Common Notations

  10. Common Derivative Notations dy d (f(x)) f’(x) dxdx Dxy y’ In this lesson, we will use y’.

  11. The derivative of a constant, or any real number is alwayszero!! y=500 y’=0

  12. POWER RULE!!!x2, 2x3 GO!

  13. Power y=axny’=naxn-1 Function *Take the power, times the function to one less power*

  14. Try it out! If y=x2, find y’. x32x2x23x3

  15. Great Job! Move On

  16. Oops! Remember….y=axny’=n·a·xn-1 Try Again

  17. Sum Rule!y=x2+3x y=3x3+4 GO!

  18. y= (f(x)+g(x))y’= f’(x)+g(x)Find the derivative of each part, just like from the power rule, and add them together!

  19. Try it out!If y=3x2+2x, find y’.6x+2x3+2x269x3+4x2

  20. Great Job! Move On

  21. Oops! Remember… y= (f(x)+g(x)) y’= f’(x)+g(x) Take derivative of each individually and add them together!! Try Again!

  22. Difference Rule!y=3x3-2 y=14x4-12x2 GO!

  23. y= f(x)-g(x)y’= f’(x)-g’(x)Find the derivative of each part and subtract respectively!

  24. Try it out!If y=12x2-24x, find y’.13x324x4824x-24

  25. Great Job! Move On

  26. Oops! Remember…It’s just like the but we subtract instead of add! Sum Rule

  27. Sum Rule y= (f(x)+g(x))y’= f’(x)+g(x)Find the derivative of each part, just like from the power rule, and add them together!

  28. Summary…Power Rule Sum Rule Difference Ruley=axny= (f(x)+g(x)) y= f(x)-g(x)y’=naxn-1 y’= f’(x)+g(x) y’= f’(x)-g’(x)

  29. Quiz Directions • You may use separate pencil and paper if needed • Click the answer you believe is correct • Keep track of how many you get correct the first try

  30. 1. y=10x3y’=20x210x30x260

  31. Great Job! Next Question

  32. Take the power times the function to one less power…y= 10x3 Power Try Again! Function

  33. 2. y=13x7y’=91x613x8x713/8 x8

  34. Great Job! Next Question

  35. Take the power times the function to one less power…y= 10x3 Power Try Again! Function

  36. 3. y=35x2+12y’=35x270x70x+1212

  37. Great Job! Next Question

  38. Take the power times the function to one less power…y= 10x3 Power Try Again! Remember… The derivative of every constant is zero!! Function

  39. 4. y=10x2+13xy’=20x2+1320x+1310x2+13x

  40. Great Job! Next Question

  41. Take the power times the function to one less power…y= 10x3 The Sum Rule says to take the derivative of each part and add them together! Power Try Again! Function

  42. 5. y=6x4+13x+20y’=24x3+1324x3+13x+2024x3+13x

  43. Great Job! Next Question

  44. Take the power times the function to one less power…y= 10x3 The Sum Rule says to take the derivative of each part and add them together! Power Try Again! Function

  45. 6. y=13x2-14xy’=13x+1426x-1413x3-14x2

  46. Great Job! Next Question

  47. Take the power times the function to one less power…y= 10x3 The Difference Rule says to take the derivative of each part and take subtract, instead of adding like the Sum Rule Power Try Again! Function

  48. 7. y=20x6-15x3-100y’=120x5-45x2120x5-45x2-10020x-15

  49. Great Job! Next Question

  50. Take the power times the function to one less power…y= 10x3 The Difference Rule says to take the derivative of each part and take subtract, instead of adding like the Sum Rule Power Try Again! Function

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