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

The derivative of 1/3*\sqrt[3]{x} is 1/(9x^{2/3)}

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

The first derivative of 1/3*\sqrt[3]{x} is 1/(9x^{2/3)}

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\frac{1}{9 x ^{\frac{2}{3}}}

Solution steps

Take the constant out:

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

Apply radical rule:

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

Simplify

\frac{1}{3} \cdot \frac{1}{3} x^{\frac{1}{3} - 1} : \frac{1}{9 x ^{\frac{2}{3}}}

= \frac{1}{9 x ^{\frac{2}{3}}}

x \to 0 lim (\frac{4 ^{x} - 1 0 ^{x}}{x})

\frac{d}{d t} (1 + cos (t))

- 2 y^{^{'}} + \frac{4 y}{x} = \frac{y ^{3}}{x}

\frac{d}{d t} (\frac{1}{t ^{2}})

\int \frac{5 x - 1}{( 2 x + 1 ) ( x - 1 )} d x

What is the derivative of 1/3*\sqrt[3]{x} ?
The derivative of 1/3*\sqrt[3]{x} is 1/(9x^{2/3)}
What is the first derivative of 1/3*\sqrt[3]{x} ?
The first derivative of 1/3*\sqrt[3]{x} is 1/(9x^{2/3)}