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anonymous

  • one year ago

how to solve this in the shortest way? finding the 10th derivative

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  1. anonymous
    • one year ago
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    find the 10th derivative of the function

  2. ganeshie8
    • one year ago
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    hmm why are u posting q in installments

  3. anonymous
    • one year ago
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    |dw:1433233107942:dw|

  4. ganeshie8
    • one year ago
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    10th derivative kills all the terms having exponent 9 and below

  5. ganeshie8
    • one year ago
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    so forget about all the terms except first |dw:1433233262560:dw|

  6. anonymous
    • one year ago
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    i will just derive the x10?

  7. ganeshie8
    • one year ago
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    since you're doing calculus, it is time to use proper notation use ^ for exponent

  8. ganeshie8
    • one year ago
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    x10 doesn't look mathematical x^10 looks better

  9. anonymous
    • one year ago
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    ow im sorry ok

  10. anonymous
    • one year ago
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    x^10 i mean

  11. ganeshie8
    • one year ago
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    yes just find the 10th derivative of that

  12. ganeshie8
    • one year ago
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    if you're careful, its not so hard to find a pattern for \(n\)th derivative of \(x^n\)

  13. anonymous
    • one year ago
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    how sir?

  14. ganeshie8
    • one year ago
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    \(\large \frac{d}{dx}(x^n) = nx^{n-1}\) \(\large \frac{d^2}{dx^2}(x^n) = n(n-1)x^{n-2}\) based on that pattern, can you guess \(\large \frac{d^{1000}}{dx^{1000}}(x^n)\) ?

  15. anonymous
    • one year ago
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    i just do the long method is the answer 3628800? is that correct?

  16. ganeshie8
    • one year ago
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    Yep! just notice 3628800 = 10*9*8*7*6*5*4*3*2*1 = 10!

  17. anonymous
    • one year ago
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    wow. wait i will answer your question the derivative of 1000

  18. ganeshie8
    • one year ago
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    Awesome! what is it

  19. anonymous
    • one year ago
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    my calculator says math error

  20. ganeshie8
    • one year ago
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    lmao

  21. anonymous
    • one year ago
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    1000! this is the answer right?

  22. ganeshie8
    • one year ago
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    do you mean \[\large \frac{d^{1000}}{dx^{1000}}(x^{1000}) = 1000!\]

  23. anonymous
    • one year ago
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    yes yes

  24. anonymous
    • one year ago
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    am i right?

  25. ganeshie8
    • one year ago
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    Looks good! thats not exactly same as the question i have asked but ok

  26. anonymous
    • one year ago
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    but u asked that earlier haha

  27. anonymous
    • one year ago
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    |dw:1433234272561:dw| is this equation true to all functions sir?

  28. anonymous
    • one year ago
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    can i use this everytime the question asks find the nth derivative?

  29. ganeshie8
    • one year ago
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    sorry thats a confusing notation... very wrong acttually, my mistake

  30. ganeshie8
    • one year ago
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    Here it is : If \(\large f(x) = x^n\), then the \(n\)th derivative is \(\large n!\)

  31. ganeshie8
    • one year ago
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    If \(\large f(x) = x^k\), then the \(k\)th derivative is \(\large k!\) btw \(k,n\) are posiitve integers

  32. anonymous
    • one year ago
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    |dw:1433234595866:dw|

  33. anonymous
    • one year ago
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    so everytime i encounter this kind of question,, i will only leave x^10? just the first term?

  34. ganeshie8
    • one year ago
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    If you're formula oriented, then yes just do that

  35. anonymous
    • one year ago
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    ooooh i understand now

  36. anonymous
    • one year ago
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    thanks again sir :-)

  37. ganeshie8
    • one year ago
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    np :) maybe work it the long way once to see why all those terms with lesser exponents don't matter for 10th derivative

  38. anonymous
    • one year ago
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    i have here many questions because i am now in my final year of engineering. that's why. so i must answer all these questions. so that i can graduate. thanks a lot sir.

  39. anonymous
    • one year ago
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    this website is a great help for me :-)

  40. ganeshie8
    • one year ago
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    ikr there is never enough time to do all the things! feel free to tag me in your future questions.. good luck!

  41. anonymous
    • one year ago
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    ok sir :-)

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