Question

section 2.4: power and sum rules for de
score: 70/180 answered: 7/18
question 8
if (f(t)=3t^{-7}), find (f(t)).
find (f(2)).
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Explanation:

Step1: Apply power - rule for differentiation

The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$. Here, $a = 3$ and $n=-7$ for $f(t)=3t^{-7}$. So, $f^\prime(t)=3\times(-7)t^{-7 - 1}$.
$f^\prime(t)=-21t^{-8}$

Step2: Evaluate $f^\prime(2)$

Substitute $t = 2$ into $f^\prime(t)$. We have $f^\prime(2)=-21\times2^{-8}$.
$f^\prime(2)=-\frac{21}{256}$

Answer:

$f^\prime(t)=-21t^{-8}$
$f^\prime(2)=-\frac{21}{256}$