What is the derivative of 7x^{1/3} ?

The derivative of 7x^{1/3} is 7/(3x^{2/3)}

What is the first derivative of 7x^{1/3} ?

The first derivative of 7x^{1/3} is 7/(3x^{2/3)}

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\frac{d}{d x} (7 x^{\frac{1}{3}})

\frac{7}{3 x ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (7 x^{\frac{1}{3}})

Take the constant out:

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

= 7 \frac{d}{d x} (x^{\frac{1}{3}})

Apply the Power Rule:

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

= 7 \cdot \frac{1}{3} x^{\frac{1}{3} - 1}

Simplify

7 \cdot \frac{1}{3} x^{\frac{1}{3} - 1} : \frac{7}{3 x ^{\frac{2}{3}}}

= \frac{7}{3 x ^{\frac{2}{3}}}

x \to 2 lim (\frac{2}{x - 2})

- \frac{1}{( 1 + x ) ^{2}}

\frac{d}{d x} (3 x^{2} - x + 12)

\int_{0}^{7} \frac{8 x}{( x - 8 ) ^{2}} d x

\int t^{\frac{1}{2}} d t

What is the derivative of 7x^{1/3} ?
The derivative of 7x^{1/3} is 7/(3x^{2/3)}
What is the first derivative of 7x^{1/3} ?
The first derivative of 7x^{1/3} is 7/(3x^{2/3)}