- Thread starter
- Admin
- #1

- Jan 26, 2012

- 4,040

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

- Thread starter Jameson
- Start date

- Thread starter
- Admin
- #1

- Jan 26, 2012

- 4,040

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

- Admin
- #2

- Jan 26, 2012

- 644

[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]

- Thread starter
- Admin
- #4

- Jan 26, 2012

- 4,040

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

- Admin
- #5

\(\displaystyle \frac{d}{dt}\left(g^n(f(t)) \right)\) 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) \(\displaystyle f(t)=p(t)\)

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

- Thread starter
- Admin
- #6

- Jan 26, 2012

- 4,040

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?