jpjones
derivative of (t-1/t)
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vf321
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For t!=0, f(t) = 1-(1/t). Do you know how to derive that?
alexray19
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Do you mean \[\frac{t-1}{t}\]
or \[t-\frac{1}{t}\]?
jpjones
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the second one
vf321
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Oh nvm forget my answer then.
alexray19
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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?
jpjones
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no i wouldn't have asked othewrwise
jpjones
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i think the derivative of t is zero
alexray19
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You don't know what the derivative of t is?
jpjones
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or 1
alexray19
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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.
jpjones
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now -1/t?
wio
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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.
alexray19
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If you know the power rule, you can use it to derive -1/t by first rewriting it as \[-t^{-1}\]
jpjones
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thank wio