What is the derivative of 1/2*\sqrt[3]{x} ?

The derivative of 1/2*\sqrt[3]{x} is 1/(6x^{2/3)}

What is the first derivative of 1/2*\sqrt[3]{x} ?

The first derivative of 1/2*\sqrt[3]{x} is 1/(6x^{2/3)}

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\frac{d}{d x} (\frac{1}{2} \cdot 3 x)

\frac{1}{6 x ^{\frac{2}{3}}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply radical rule:

n a = a^{\frac{1}{n}}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{1}{2} \cdot \frac{1}{3} x^{\frac{1}{3} - 1}

Simplify

\frac{1}{2} \cdot \frac{1}{3} x^{\frac{1}{3} - 1} : \frac{1}{6 x ^{\frac{2}{3}}}

= \frac{1}{6 x ^{\frac{2}{3}}}

\int_{0}^{1} e^{- 3 x} d x

\frac{\partial}{\partial x} (\frac{1}{y} - 2 x sin (y))

\frac{d}{d x} (\frac{( e ^{x} - 1 )}{x})

y^{^{''}} - y^{^{'}} - 2 y = - 2 t + 6 t^{2}

\frac{d}{d x} (e^{s i n^{2} (x)})

What is the derivative of 1/2*\sqrt[3]{x} ?
The derivative of 1/2*\sqrt[3]{x} is 1/(6x^{2/3)}
What is the first derivative of 1/2*\sqrt[3]{x} ?
The first derivative of 1/2*\sqrt[3]{x} is 1/(6x^{2/3)}