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Johan14th

  • one year ago

Can i get help to solve for the derivative of f(x)= x^4 +1

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  1. Vocaloid
    • one year ago
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    derivative rule for exponents: the derivative of x^n is n*x^(n-1)

  2. Vocaloid
    • one year ago
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    also, the derivative of 1 is 0 since 1 is a constant

  3. Vocaloid
    • one year ago
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    unless you want to find the derivative using the (x+h) method?

  4. Johan14th
    • one year ago
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    just an extra question but would the derivative of theta equal 1|dw:1443659495630:dw|

  5. Vocaloid
    • one year ago
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    yes

  6. Vocaloid
    • one year ago
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    (theta can be used like a variable, just like x)

  7. Johan14th
    • one year ago
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    i tried the x+h method and received a wrong answer so i will try the first way you talked about

  8. Vocaloid
    • one year ago
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    x + h method will always give the right answer

  9. Johan14th
    • one year ago
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    i just have problems keeping my division right with powers

  10. Vocaloid
    • one year ago
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    let's try the x + h method first, then I'll show you the "shortcut method" afterwords

  11. Johan14th
    • one year ago
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    alright

  12. Vocaloid
    • one year ago
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    |dw:1443659654089:dw|

  13. Vocaloid
    • one year ago
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    |dw:1443659860105:dw|

  14. Vocaloid
    • one year ago
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    now, if you're wondering how I got from (x+h)^4 to that huge expression, I used Pascal's triangle (if you don't know it already, I highly suggest learning about it! it saves tons of time)

  15. Johan14th
    • one year ago
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    we've barely seen it in class, weird enough it was for engineering and not calculus, but now i will try to learn it ahead of time. thank you

  16. Vocaloid
    • one year ago
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    anyhoo, we cancel out the x^4 and the -x^4 next|dw:1443660131464:dw|

  17. Vocaloid
    • one year ago
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    then we factor out h from the numerator

  18. Vocaloid
    • one year ago
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    |dw:1443660161997:dw|

  19. Vocaloid
    • one year ago
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    then we cancel out h to get|dw:1443660211856:dw|

  20. Vocaloid
    • one year ago
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    then we set h = 0 to get|dw:1443660231771:dw|

  21. Johan14th
    • one year ago
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    alright i think i finally got a hand of this. i was just really confused in class but this explains everything nice and easy thanks again.

  22. Vocaloid
    • one year ago
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    no problem! Later on in class, you'll learn tricks and rules that will make this much easier

  23. Vocaloid
    • one year ago
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    so, like I promised, I can show you a faster method to get the same answer

  24. Vocaloid
    • one year ago
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    |dw:1443660442174:dw|

  25. Vocaloid
    • one year ago
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    the derivative of 1 is 0, since 1 is a constant (no variable attached to it)

  26. Vocaloid
    • one year ago
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    and, like I said before, the derivative of x^n is n*x^(n-1)

  27. Vocaloid
    • one year ago
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    |dw:1443660601884:dw|

  28. Vocaloid
    • one year ago
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    none of that icky x + h stuff, haha :P

  29. Johan14th
    • one year ago
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    Haha well this just made my hour of calculus struggle and the 10 trees i had to sacrifice for the paper really lame ...

  30. Vocaloid
    • one year ago
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    I had to do that, too, lol. I think most calc teachers start off with the x + h method just to emphasize the idea of what a derivative really is (the rate of change over a small interval h)

  31. Johan14th
    • one year ago
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    yes unfortunately for me this also involves a dozen of cheesy math songs that get stuck in your head all day.

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