What is the derivative of (5x)^{1/3} ?

The derivative of (5x)^{1/3} is (5^{1/3})/(3x^{2/3)}

What is the first derivative of (5x)^{1/3} ?

The first derivative of (5x)^{1/3} is (5^{1/3})/(3x^{2/3)}

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derivative

\frac{5 ^{\frac{1}{3}}}{3 x ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} ((5 x)^{\frac{1}{3}})

Simplify

(5 x)^{\frac{1}{3}} : 5^{\frac{1}{3}} x^{\frac{1}{3}}

= \frac{d}{d x} (5^{\frac{1}{3}} x^{\frac{1}{3}})

Take the constant out:

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

= 5^{\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}

= 5^{\frac{1}{3}} \cdot \frac{1}{3} x^{\frac{1}{3} - 1}

Simplify

5^{\frac{1}{3}} \cdot \frac{1}{3} x^{\frac{1}{3} - 1} : \frac{5 ^{\frac{1}{3}}}{3 x ^{\frac{2}{3}}}

= \frac{5 ^{\frac{1}{3}}}{3 x ^{\frac{2}{3}}}

What is the derivative of (5x)^{1/3} ?
The derivative of (5x)^{1/3} is (5^{1/3})/(3x^{2/3)}
What is the first derivative of (5x)^{1/3} ?
The first derivative of (5x)^{1/3} is (5^{1/3})/(3x^{2/3)}