Step 1 Recall the Chain Rule in terms of the functions $$ h(x) $$ and $$ g(x) $$, which states that if $$ g $$ is differentiable at $$ x $$ and $$ h $$ is differentiable at $$ g(x) $$, then the composite function $$ F=h $$ o $$ g $$ defined by $$ F(x)=h(g(x)) $$ is differentiable at $$ x $$ and $$ F^{\prime} $$ is given by the following. $$ F^{\prime}(x)=h^{\prime}(g(x)) \cdot g^{\prime}(x) $$ We are given the function $$ f(x)=\sin (8 \ln (x)) $$ To write this is the form $$ F(x)=h(g(x)) $$ we can let $$ g(x)=8 \ln (x) $$ and $$ h(x)= $$ SUBMI SUB (YOU CANNOT COME BACK) Need Help? Read It SUBMIT ANSWER SKI

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UpStudy AI · Accepted Answer

Given that we want to write  
$$
f(x) = \sin(8\ln(x))
$$  
in the form  
$$
F(x) = h(g(x)),
$$  
we can identify  
$$
g(x)=8\ln(x)
$$  
and hence  
$$
h(x) = \sin(x).
$$
$$ h(x) = \sin(x) $$

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