What is the derivative of \sqrt[n]{x} ?

The derivative of \sqrt[n]{x} is (x^{(1-n)/n})/(n)

What is the first derivative of \sqrt[n]{x} ?

The first derivative of \sqrt[n]{x} is (x^{(1-n)/n})/(n)

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\frac{x ^{\frac{1 - n}{n}}}{n}

Solution steps

Apply radical rule:

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

Apply the Power Rule:

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

= \frac{1}{n} x^{\frac{1}{n} - 1}

Simplify

\frac{1}{n} x^{\frac{1}{n} - 1} : \frac{x ^{\frac{1 - n}{n}}}{n}

= \frac{x ^{\frac{1 - n}{n}}}{n}

What is the derivative of \sqrt[n]{x} ?
The derivative of \sqrt[n]{x} is (x^{(1-n)/n})/(n)
What is the first derivative of \sqrt[n]{x} ?
The first derivative of \sqrt[n]{x} is (x^{(1-n)/n})/(n)