section 2.4: power and sum rules for de\nscore: 70/180 answered: 7/18\nquestion 8\nif (f(t)=3t^{-7}), find…

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:

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