Vanessa Woodley

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by Vanessa Woodley5 views·Updated Apr 10, 2021
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Differentiating Using the Power Rule

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  1. Hi everyone.
  2. I'm Miss Woodley.
  3. And today we're going to apply the power rule which
  4. is basic differentiation.
  5. So we're going to differentiate today appreciation.
  6. Using the power.
  7. Okay now when we say power rule, if we have
  8. a function such as X.
  9. To the fourth here we have a power.
  10. If we need to differentiate this dough notation to uses
  11. D. The X.
  12. Of this to apply the power rule.
  13. What we do is bring down the power of four
  14. to the front and multiply will bring down the four
  15. and reduce the exponent by one.
  16. So we have four X to the third.
  17. Bring down the power, reduce it by one.
  18. Let us look at another example.
  19. For instance if we have two X cube, how will
  20. we differentiate this?
  21. Went down The three multiplied by two.
  22. So that will give us six and reducing three by
  23. one. That's still yes.
  24. Let us look at another scenario.
  25. What if we have just three X.
  26. How do we differentiate this?
  27. No, the same thing applies the power rule X is
  28. the same thing as X to the one power.
  29. So if you have to bring that one and multiply
  30. by three you have three reducing the power Of one
  31. x 1.
  32. We have zero.
  33. Now we should know that anything to the zero power
  34. is one.
  35. So this is the same thing as three times one
  36. which is equals 23 So if you are ever given
  37. any situation where you just have to differentiate um let's
  38. say six X.
  39. We should know about the answer to that is just
  40. six. Okay.
  41. Okay. Let's look at um another scenario.
  42. How about if you're just given a constant to differentiate?
  43. Such as for the derivative of four, were we differentiate
  44. in any constant?
  45. It cancels off to zero.
  46. Now we were to go into the details of that.
  47. This could be the same thing as multiplying by X
  48. to the zero power.
  49. And we know anything to the zero power is why?
  50. So if we're to bring down the zero and multiplied
  51. by four, we have zero.
  52. So there's no need to go any further there.
  53. Okay, so let us See if you will not derivative
  54. of face.
  55. What if you're given the the X.
  56. of seven the derivative of that in zero.
  57. Great. Now let's look at um Home extended polynomial were
  58. given the function of three X squared minus two.
  59. X plus floor.
  60. And we need to differentiate this.
  61. Now here I'll give you as a function where Y.
  62. Z equals to this polynomial.
  63. In this case the notation to write the derivative of
  64. Y is the Y.
  65. The X.
  66. The derivative of white.
  67. In terms of X.
  68. Now to differentiate this, you have to differentiate the path.
  69. We have three paths to this polynomial.
  70. So first we'll differentiate that.
  71. So you bring down the two.
  72. You multiply by three.
  73. We have six X.
  74. And to do fresh eight negative to that will be
  75. negative two and four which is a constant has begun
  76. as zero.
  77. Great job.
  78. Right. Let us look at some more scenarios to differentiate.
  79. Um Yeah.
  80. What if you have to differentiate Y equals to exit
  81. a 3/2?
  82. We have an exponent which is a power.
  83. I mean a fraction.
  84. So to differentiate this D.
  85. Y. X.
  86. We will bring down that multiply and then reduce it
  87. by one.
  88. If we have few over two minus one Representing this
  89. one as a whole number with the same denominator.
  90. Well b minus 2/2.
  91. So then we'll have the over two X.
  92. If you take away too from three you have a
  93. half. So they're the derivative of X And 3/2.
  94. Is this now another thing that you have to note
  95. with differentiation is instead of using the white X.
  96. We might need to go a shorter use a shorter
  97. notation. So we'll say why prime?
  98. This means the first derivative of Hawaii.
  99. Okay. Which is instead of using this sometimes we can
  100. just write White prime.
  101. Just show on to.
  102. All right.
  103. Now, let's look at some other scenarios.
  104. What if we need to differentiate the square root of
  105. X? Now, we should know that the square root of
  106. X can be rewritten as X and a half power.
  107. Yeah. So based on what we just did to differentiate
  108. that using the shot the shop notation, I'm gonna just
  109. say white prime.
  110. You bring down the half and you reduce half by
  111. one. So if you have a half when you take
  112. away one, which is two too, we'll have a half
  113. one minus two.
  114. That's negative 1/2.
  115. So that's the derivative of the square root of X.
  116. I have exit minus behalf.
  117. Great job.
  118. Now let's look at maybe some other scenarios.
  119. Mm hmm.
  120. What if we want to differentiate?
  121. Um why equals?
  122. Let's use a negative, explain it this time?
  123. So D.
  124. Y. The X is equal to negative three X.
  125. If you have negative three and we have to take
  126. away one.
  127. What happens here?
  128. We add to negative and make it negative.
  129. So there we are applying the power rule for differentiation.