Question

derivative rules with table of values
score: 1/5 penalty: none
question
use the chart to find (h(4)) in simplest form.
\begin{tabular}{|c|c|c|}hline$x$&4&3\hline$f(x)$&4&12\hline$f(x)$& - 8&1\hline$g(x)$&3&2\hline$g(x)$&7& - 5\hlineend{tabular}
$h(x)=f(g(x))$
answer
attempt 1 out of 2
$h(4)=$

Explanation:

Step1: Recall the chain - rule formula

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

Step2: Find $g(4)$

From the table, when $x = 4$, $g(4)=3$.

Step3: Find $f^{\prime}(g(4))$

Since $g(4)=3$, we need to find $f^{\prime}(3)$. From the table, $f^{\prime}(3)=1$.

Step4: Find $g^{\prime}(4)$

From the table, when $x = 4$, $g^{\prime}(4)=7$.

Step5: Calculate $h^{\prime}(4)$

Using the chain - rule $h^{\prime}(4)=f^{\prime}(g(4))\cdot g^{\prime}(4)$. Substitute $f^{\prime}(g(4)) = 1$ and $g^{\prime}(4)=7$ into the formula. So $h^{\prime}(4)=1\times7 = 7$.

Answer:

$7$