Find the derivative using the chain rule.
\[
f(k)=\sqrt{2 k^{9}+7}
\]
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Hint: To add the square root symbol $(\sqrt{\square})$, type "root"

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Answer

$\boxed{f'(k) = \frac{9k^8}{\sqrt{2k^9 + 7}}}$

Steps

Step 1 ：Find the derivative of the function using the chain rule: $f'(k) = \frac{1}{2\sqrt{2k^9 + 7}} \cdot 18k^8$

Step 2 ：Simplify the expression: $f'(k) = \frac{9k^8}{\sqrt{2k^9 + 7}}$

Step 3 ：Evaluate the derivative for a given value of k (e.g., k = 2): $f'(2) \approx 71.755$

Step 4 ：$\boxed{f'(k) = \frac{9k^8}{\sqrt{2k^9 + 7}}}$