For the composite function $$ f(x)=g(h(x)) $$, identify an inside and outside function. Write the derivative of the composite function with respect to $$ x $$. Do not use identity functions for $$ g(h) $$ or $$ h(x) $$. $$ f(x)=3^{\ln (x)} $$ $$ \{g(h), h(x)\}=\{ $$ $$ f^{\prime}(x)= $$

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For the function $$ f(x) = 3^{\ln(x)} $$, we can identify the inside and outside functions as follows:
- Inside function $$ h(x) = \ln(x) $$
- Outside function $$ g(h) = 3^{h} $$

Thus, we have:
$$
\{g(h), h(x)\} = \{3^{h}, \ln(x)\}
$$
To find the derivative $$ f'(x) $$ of the composite function $$ f(x) = g(h(x)) $$, we will use the chain rule:
$$
f'(x) = g'(h(x)) \cdot h'(x)
$$

First, we need to find $$ g'(h) $$ and $$ h'(x) $$:
1. $$ g(h) = 3^{h} $$ implies $$ g'(h) = 3^{h} \ln(3) $$
2. $$ h(x) = \ln(x) $$ implies $$ h'(x) = \frac{1}{x} $$

Now we can substitute these into the derivative formula:
$$
f'(x) = g'(\ln(x)) \cdot h'(x) = 3^{\ln(x)} \ln(3) \cdot \frac{1}{x}
$$
Thus, the derivative of the composite function is: $$ f'(x) = \frac{3^{\ln(x)} \ln(3)}{x} $$ And the identified functions are: $$ \{g(h), h(x)\} = \{3^{h}, \ln(x)\} $$

For the composite function , identify an inside and outside function. Write the derivative of the composite function with respect to . Do
not use identity functions for or .

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For the composite function , identify an inside and outside function. Write the derivative of the composite function with respect to . Do not use identity functions for or .