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jpjones

  • 3 years ago

derivative of (t-1/t)

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  1. vf321
    • 3 years ago
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    For t!=0, f(t) = 1-(1/t). Do you know how to derive that?

  2. alexray19
    • 3 years ago
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    Do you mean \[\frac{t-1}{t}\] or \[t-\frac{1}{t}\]?

  3. jpjones
    • 3 years ago
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    the second one

  4. vf321
    • 3 years ago
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    Oh nvm forget my answer then.

  5. alexray19
    • 3 years ago
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    Well you're just doing two separate derivatives then. One for t, and one for -1/t. Can you do these separately?

  6. jpjones
    • 3 years ago
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    no i wouldn't have asked othewrwise

  7. jpjones
    • 3 years ago
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    i think the derivative of t is zero

  8. alexray19
    • 3 years ago
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    You don't know what the derivative of t is?

  9. jpjones
    • 3 years ago
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    or 1

  10. alexray19
    • 3 years ago
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    No, 0 is only the derivative of a constant. For example, the derivative of the number 5 is 0. t is a variable that changes, so its derivative can't be 0 (that would imply it's not changing). Yes, 1 is correct for t.

  11. jpjones
    • 3 years ago
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    now -1/t?

  12. wio
    • 3 years ago
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    Use to power rule: \[\frac{d}{dx}x^n = n\cdot x^{n-1}\] In the first case, n = 1, and in the second case n = -1.

  13. alexray19
    • 3 years ago
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    If you know the power rule, you can use it to derive -1/t by first rewriting it as \[-t^{-1}\]

  14. jpjones
    • 3 years ago
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    thank wio

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