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

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

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

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

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derivative of

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

Solution steps

Apply radical rule:

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

Apply the Power Rule:

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

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

Simplify

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

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

f (x) = e^{9}

w \to a lim (\frac{a ^{2} - w ^{2}}{a - w})

\int e^{1 - 5 x} d x

e^{- 2.5 s}

\int_{0}^{2} (x^{3} - 4 x) d x

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