Find the value of the given function's derivative at $$ x=2 $$. $$ \begin{aligned} f(x) & =k(g(x)) \ g(2) & =16 \ g^{\prime}(2) & =1 \ k(6) & =2 \ k^{\prime}(16) & =7 \ f^{\prime}(2) & =[?]\end{aligned} $$

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We are given the function $$ f(x) = k(g(x)) $$ and need to find $$ f'(2) $$.

Using the chain rule, we write:
$$
f'(x) = k'(g(x)) \cdot g'(x)
$$

Evaluating at $$ x = 2 $$:
$$
f'(2) = k'(g(2)) \cdot g'(2)
$$

Substitute the given values:
$$
g(2) = 16 \quad \text{and} \quad g'(2) = 1
$$
$$
f'(2) = k'(16) \cdot 1
$$

Since $$ k'(16) = 7 $$, we have:
$$
f'(2) = 7
$$
$$ f'(2) = 7 $$

Find the value of the given
function’s derivative at .

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Find the value of the given function’s derivative at .