Question

question 15 · 1 point
for ( j(x)=f(x)cdot g(x)), use the product - rule to find ( j(-8)) if ( f(-8)=-7), ( f(-8)=-5), ( g(-8)=8), and ( g(-8)=1).
provide your answer below:
( j(-8)=square)

Explanation:

Step1: Recall the product - rule

The product - rule states that if $j(x)=f(x)\cdot g(x)$, then $j^{\prime}(x)=f^{\prime}(x)g(x)+f(x)g^{\prime}(x)$.

Step2: Substitute $x = - 8$

We are given that $f(-8)=-7$, $f^{\prime}(-8)=-5$, $g(-8)=8$, and $g^{\prime}(-8)=1$.
Substitute these values into the product - rule formula:
$j^{\prime}(-8)=f^{\prime}(-8)g(-8)+f(-8)g^{\prime}(-8)$.
$j^{\prime}(-8)=(-5)\times8+(-7)\times1$.

Step3: Calculate the result

First, calculate $(-5)\times8=-40$ and $(-7)\times1=-7$.
Then, $j^{\prime}(-8)=-40 - 7=-47$.

Answer:

$-47$