Compute the derivatives of the given functions.
a) $f(x)=\ln \left(2 x^{4}\right), \quad f^{\prime}(x)=$
b) $g(x)=\ln (\sqrt[5]{x}), \quad g^{\prime}(x)=$

Answer

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Answer

$\boxed{g'(x) = \frac{1}{5x}}$

Steps

Step 1 ：$ \frac{d}{dx}(\ln (2x^{4})) = \frac{1}{2x^{4}} \frac{d}{dx}(2x^{4}) $

Step 2 ：$ = \frac{1}{2x^{4}}(8x^{3}) $

Step 3 ：$ = \frac{4}{x} $

Step 4 ：$ \frac{d}{dx}(\ln (x^{1/5})) = \frac{1}{x^{1/5}} \frac{d}{dx}(x^{1/5}) $

Step 5 ：$ = \frac{1}{x^{1/5}}(\frac{1}{5}x^{-4/5}) $

Step 6 ：$ = \frac{1}{5x} $

Step 7 ：$\boxed{f'(x) = \frac{4}{x}}$

Step 8 ：$\boxed{g'(x) = \frac{1}{5x}}$