What is the derivative of \sqrt[3]{(3x/(4pi)}) ?

The derivative of \sqrt[3]{(3x/(4pi)}) is 1/(3^{2/3)*4^{1/3}pi^{1/3}x^{2/3}}

What is the first derivative of \sqrt[3]{(3x/(4pi)}) ?

The first derivative of \sqrt[3]{(3x/(4pi)}) is 1/(3^{2/3)*4^{1/3}pi^{1/3}x^{2/3}}

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\frac{1}{3 ^{\frac{2}{3}} \cdot 4 ^{\frac{1}{3}} π ^{\frac{1}{3}} x ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

\frac{1}{3 ( \frac{3 x}{4 π} ) ^{\frac{2}{3}}} \frac{d}{d x} (\frac{3 x}{4 π})

= \frac{1}{3 ( \frac{3 x}{4 π} ) ^{\frac{2}{3}}} \frac{d}{d x} (\frac{3 x}{4 π})

\frac{d}{d x} (\frac{3 x}{4 π}) = \frac{3}{4 π}

= \frac{1}{3 ( \frac{3 x}{4 π} ) ^{\frac{2}{3}}} \cdot \frac{3}{4 π}

Simplify

\frac{1}{3 ( \frac{3 x}{4 π} ) ^{\frac{2}{3}}} \cdot \frac{3}{4 π} : \frac{1}{3 ^{\frac{2}{3}} \cdot 4 ^{\frac{1}{3}} π ^{\frac{1}{3}} x ^{\frac{2}{3}}}

= \frac{1}{3 ^{\frac{2}{3}} \cdot 4 ^{\frac{1}{3}} π ^{\frac{1}{3}} x ^{\frac{2}{3}}}

What is the derivative of \sqrt[3]{(3x/(4pi)}) ?
The derivative of \sqrt[3]{(3x/(4pi)}) is 1/(3^{2/3)*4^{1/3}pi^{1/3}x^{2/3}}
What is the first derivative of \sqrt[3]{(3x/(4pi)}) ?
The first derivative of \sqrt[3]{(3x/(4pi)}) is 1/(3^{2/3)*4^{1/3}pi^{1/3}x^{2/3}}