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Learn how to apply the Power Rule in calculus with step-by-step examples and explanations. Master differentiation with this comprehensive guide.

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  1. = • (7x+2)13/13 • (7x+2)13/13 + C • (7x+2)11/13 + C • (7x+2)11/11 + C

  2. = • (7x+2)13/13 • (7x+2)13/13 + C • (7x+2)11/13 + C • (7x+2)11/11 + C

  3. .

  4. . u = 2x-3 du/dx = 2 du = 2 dx du/2 = dx

  5. Power Rule • If u is any differentiable function and n is not -1, then

  6. Let u = the bad stuff • Using the power rule • u = 1 + z2. • du/dz = 2z or du = 2z dz • z dz = du/2

  7. Let u = the bad stuff • u = 1 + z2. • du/dz = 2z • z dz = du/2

  8. u = du/df = 7 or du = 7 df Anti Chain Rule

  9. . u = du/dx = du = 3x2dx x2dx = du/3

  10. sin(3x) dx = • u = 3x • du = 3 dx • 1/3 du = dx

  11. sin 3x dx u = • sin 3x • x • 3x • cos 3x

  12. sin 3x dx u = • sin 3x • x • 3x • cos 3x

  13. sin(3x) dx = • u = 3x • du = 3 dx • 1/3 du = dx

  14. u = 2x-3 (2x-3)3dx • du/dx = 2 • du = 2 dx • du/2 = dx u3 /2 du =

  15. (2x-3)3dx u = • 2x - 3 • 2x • 3x • (2x – 3)3

  16. (2x-3)3dx u = • 2x - 3 • 2x • 3x • (2x – 3)3

  17. (2x-3)3dx u = 2x-3 du = • 2 dx • 0 dx • 3 dx • -3 dx

  18. (2x-3)3dx u = 2x-3 du = • 2 dx • 0 dx • 3 dx • -3 dx

  19. (u)3 ½ du = (2x-3)3dx • Replace 2x-3 with u, dx by 2 du • Replace 2x-3 with u, dx by ½ du • Replace (2x-3)3 with u, dx by ½ du

  20. (u)3 ½ du = (2x-3)3dx • Replace 2x-3 with u, dx by 2 du • Replace 2x-3 with u, dx by ½ du • Replace (2x-3)3 with u, dx by ½ du

  21. u = 2x-3 (2x-3)3dx = • (2x-3)4/4 + c • u4/8 + c • (2x-3)4/8 + c • 2(2x-3)4 + c

  22. u = 2x-3 (2x-3)3dx = • (2x-3)4/4 + c • u4/8 + c • (2x-3)4/8 + c • 2(2x-3)4 + c

  23. =

  24. = • 0.333333 • 0.1

  25. x sec2(3x2)dx u = • sec 3x2 • 3x • 3x2 • x

  26. x sec2(3x2)dx u = • sec 3x2 • 3x • 3x2 • x

  27. u = 3x2 x sec2(3x2)dx • du/dx = 6x • du = 6x dx • du/6 = x dx 1/6 sec2(u) du =

  28. x sec2(3x2)dx • tan 3x2 + c • tan 3x2/ 3 + c • sec 3x2/ 3 + c • tan 3x2/ 6 + c

  29. x sec2(3x2)dx • tan 3x2 + c • tan 3x2/ 3 + c • sec 3x2/ 3 + c • tan 3x2/ 6 + c

  30. Copy g(x) If derivative is here Add one to exponent Divide by new exponent Anti Power Rule

  31. = • Check help on next slide

  33. =

  34. = • 0.2 • 0.1

  35. =

  36. = • -10.0 • 0.1

  37. =

  38. = • 0.5 • 0.1

  39. What is the derivative of tan(x)?

  40. What is the derivative of tan(x)?

  41. Copy sin(x) Derivative is here Add one to exponent Divide by new exponent Anti Power Rule

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