Find the derivative using the chain rule.
\[
f(a)=\sqrt{8 a^{7}+6}
\]

Answer

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Answer

\(\boxed{f'(a) = \frac{14\sqrt{2}a^6}{\sqrt{4a^7 + 3}}}\)

Steps

Step 1 ：Find the derivative of the outer function: \(\frac{1}{2\sqrt{8a^7 + 6}}\)

Step 2 ：Find the derivative of the inner function: \(56a^6\)

Step 3 ：Apply the chain rule: \(\frac{1}{2\sqrt{8a^7 + 6}} \cdot 56a^6\)

Step 4 ：Simplify the expression: \(\frac{14\sqrt{2}a^6}{\sqrt{4a^7 + 3}}\)

Step 5 ：\(\boxed{f'(a) = \frac{14\sqrt{2}a^6}{\sqrt{4a^7 + 3}}}\)