What is the derivative of 3x^{1/3} ?

The derivative of 3x^{1/3} is 1/(x^{2/3)}

What is the first derivative of 3x^{1/3} ?

The first derivative of 3x^{1/3} is 1/(x^{2/3)}

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

y^{^{''}} + 2 y^{^{'}} - 35 y = 0

x \to 5 - lim (\frac{8}{x - 5})

y = 6^{- 4 x}

\frac{d}{d t} (e^{t} t)

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

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