What is the derivative of \sqrt[3]{{g}(x}) ?

The derivative of \sqrt[3]{{g}(x}) is (derivative of {g}(x))/(3{g)(x)^{2/3}}

What is the first derivative of \sqrt[3]{{g}(x}) ?

The first derivative of \sqrt[3]{{g}(x}) is (derivative of {g}(x))/(3{g)(x)^{2/3}}

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\frac{\frac{d}{d x} ( g ( x ) )}{3 g ( x ) ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

\frac{1}{3 g ( x ) ^{\frac{2}{3}}} \frac{d}{d x} (g (x))

= \frac{1}{3 g ( x ) ^{\frac{2}{3}}} \frac{d}{d x} (g (x))

Simplify

\frac{1}{3 g ( x ) ^{\frac{2}{3}}} \frac{d}{d x} (g (x)) : \frac{\frac{d}{d x} ( g ( x ) )}{3 g ( x ) ^{\frac{2}{3}}}

= \frac{\frac{d}{d x} ( g ( x ) )}{3 g ( x ) ^{\frac{2}{3}}}

What is the derivative of \sqrt[3]{{g}(x}) ?
The derivative of \sqrt[3]{{g}(x}) is (derivative of {g}(x))/(3{g)(x)^{2/3}}
What is the first derivative of \sqrt[3]{{g}(x}) ?
The first derivative of \sqrt[3]{{g}(x}) is (derivative of {g}(x))/(3{g)(x)^{2/3}}