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

Answer

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Answer

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

Steps

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

Step 2 ：Find the derivative of the inner function: $56 a^{6}$

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

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

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