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

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

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

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

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

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

Solution steps

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

Simplify

1 \cdot 3 x : 3 x

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

Apply radical rule:

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

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

Simplify

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

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

\frac{\partial}{\partial x} (2 ln (x^{2} + y^{2}))

arccsc (- t^{2})

x \to 0 lim (sin (\frac{3 π}{x}))

\frac{\partial}{\partial x} (e^{x + t})

\frac{\partial}{\partial x} (6 e^{x y})

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