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- #1

- Jan 26, 2012

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Calculate __________ for each $v_1, v_2, v_3$ and $p(t)$.

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- Thread starter
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- #1

- Jan 26, 2012

- 4,058

Calculate __________ for each $v_1, v_2, v_3$ and $p(t)$.

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- #2

- Jan 26, 2012

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[JUSTIFY]But without the context of the actual calculation, it's hard to be certain, especially when the question is written in plain English like this. In formal notation, there would be no ambiguity, for instance, but in English, it could have many different interpretations.[/JUSTIFY]

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- Jan 26, 2012

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Calculate ________ for $1+t^2, 2-t+3t^2, 4+t$ and $p(t)$.

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\(\displaystyle \frac{d}{dt}\left(g^n(f(t)) \right)\) and so they would do the following:

First, the student would find via the power and chain rules:

\(\displaystyle \frac{d}{dt}\left(g^n(f(t)) \right)=ng^{n-1}(f(t))\cdot f'(t)\)

i) \(\displaystyle f(t)=1+t^2\)

\(\displaystyle \frac{d}{dt}\left(g^n(1+t^2) \right)=ng^{n-1}(1+t^2)\cdot(2t)\)

ii) \(\displaystyle f(t)=2-t+3t^2\)

\(\displaystyle \frac{d}{dt}\left(g^n(2-t+3t^2) \right)=ng^{n-1}(2-t+3t^2)\cdot(6t-1)\)

iii) \(\displaystyle f(t)=4+t\)

\(\displaystyle \frac{d}{dt}\left(g^n(4+t) \right)=ng^{n-1}(4+t)\cdot(1)\)

iv) \(\displaystyle f(t)=p(t)\)

\(\displaystyle \frac{d}{dt}\left(g^n(p(t)) \right)=ng^{n-1}(p(t))\cdot p'(t)\)

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- #6

- Jan 26, 2012

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Here's one thing to ponder and again, sorry this is cryptic but I don't want to influence your thoughts too much:

Are there 4 terms or 3 terms to calculate?