Why is the derivative of $x^2$ equal to $2x$ rather than $4x$?

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Between 2m26s and 4m36s of this YouTube video, the teacher explains the power rule using the area of a square.



  1. But why isnt the square or cube increasing its area or volume on all sides?


  2. If square increases its area by all 4sides, shouldnt the derivative be 4x dx ?? whats the argument behind this???


Thanks.




calculus derivatives




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    Between 2m26s and 4m36s of this YouTube video, the teacher explains the power rule using the area of a square.



    1. But why isnt the square or cube increasing its area or volume on all sides?


    2. If square increases its area by all 4sides, shouldnt the derivative be 4x dx ?? whats the argument behind this???


    Thanks.




    calculus derivatives




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      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      Between 2m26s and 4m36s of this YouTube video, the teacher explains the power rule using the area of a square.



      1. But why isnt the square or cube increasing its area or volume on all sides?


      2. If square increases its area by all 4sides, shouldnt the derivative be 4x dx ?? whats the argument behind this???


      Thanks.




      calculus derivatives




      share|cite|improve this question














      Between 2m26s and 4m36s of this YouTube video, the teacher explains the power rule using the area of a square.



      1. But why isnt the square or cube increasing its area or volume on all sides?


      2. If square increases its area by all 4sides, shouldnt the derivative be 4x dx ?? whats the argument behind this???


      Thanks.





      calculus derivatives





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      edited Aug 21 at 9:07









      Rodrigo de Azevedo

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      asked Aug 21 at 9:01









      Yogi

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          That's because the core thing which is happening is not that the square / cube is padded on one side, but that the side lengths of the square / cube are increasing by $dx$. We could have it expand in both directions, but then each padding would be $frac12dx$ thick. You would get the same result.






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          • Now I understand, Thanks for clearing me out... :)
            – Yogi
            Aug 21 at 9:16










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          up vote
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          That's because the core thing which is happening is not that the square / cube is padded on one side, but that the side lengths of the square / cube are increasing by $dx$. We could have it expand in both directions, but then each padding would be $frac12dx$ thick. You would get the same result.






          share|cite|improve this answer




















          • Now I understand, Thanks for clearing me out... :)
            – Yogi
            Aug 21 at 9:16














          up vote
          8
          down vote



          accepted










          That's because the core thing which is happening is not that the square / cube is padded on one side, but that the side lengths of the square / cube are increasing by $dx$. We could have it expand in both directions, but then each padding would be $frac12dx$ thick. You would get the same result.






          share|cite|improve this answer




















          • Now I understand, Thanks for clearing me out... :)
            – Yogi
            Aug 21 at 9:16












          up vote
          8
          down vote



          accepted







          up vote
          8
          down vote



          accepted






          That's because the core thing which is happening is not that the square / cube is padded on one side, but that the side lengths of the square / cube are increasing by $dx$. We could have it expand in both directions, but then each padding would be $frac12dx$ thick. You would get the same result.






          share|cite|improve this answer












          That's because the core thing which is happening is not that the square / cube is padded on one side, but that the side lengths of the square / cube are increasing by $dx$. We could have it expand in both directions, but then each padding would be $frac12dx$ thick. You would get the same result.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Aug 21 at 9:03









          Arthur

          101k794176




          101k794176











          • Now I understand, Thanks for clearing me out... :)
            – Yogi
            Aug 21 at 9:16
















          • Now I understand, Thanks for clearing me out... :)
            – Yogi
            Aug 21 at 9:16















          Now I understand, Thanks for clearing me out... :)
          – Yogi
          Aug 21 at 9:16




          Now I understand, Thanks for clearing me out... :)
          – Yogi
          Aug 21 at 9:16












           

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