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}}}

\frac{d}{d x} (sin^{9} (cos (8 x)))

\int (8 x + 15) ln (2 x) d x

\int t^{2} e^{- 9 t} d t

\int_{1}^{4} \frac{3 ln ( x )}{x ^{2}} d x

\frac{d}{d x} (\frac{x ^{4}}{9})

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}}