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

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

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

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

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

Solution steps

Apply the chain rule:

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

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

\frac{d}{d x} (π x) = π

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

Simplify

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

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

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

\frac{y}{y - x}

\frac{d}{d x} (ln (x - 1) + cos (x - 1))

\int_{- 1}^{1} 1 - x^{2} d x

\int cos (4 x + 2) d x

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