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

The derivative of 2/(3\sqrt[3]{x}) is -2/(9x^{4/3)}

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

The first derivative of 2/(3\sqrt[3]{x}) is -2/(9x^{4/3)}

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

- \frac{2}{9 x ^{\frac{4}{3}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Simplify

\frac{2}{3} (- \frac{1}{3} x^{- \frac{1}{3} - 1}) : - \frac{2}{9 x ^{\frac{4}{3}}}

= - \frac{2}{9 x ^{\frac{4}{3}}}

\int - 0.2 t^{2} + 3 d t

\frac{\partial}{\partial x} (sin (π \cdot x))

\int x sin (x y) d y

\frac{d}{d x} (cos^{3} (4 x))

x \to 2 lim (x^{3} + 2 x + 1)

What is the derivative of 2/(3\sqrt[3]{x}) ?
The derivative of 2/(3\sqrt[3]{x}) is -2/(9x^{4/3)}
What is the first derivative of 2/(3\sqrt[3]{x}) ?
The first derivative of 2/(3\sqrt[3]{x}) is -2/(9x^{4/3)}